Chapter 5 Resource Masters
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1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11
CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish.
MHID ISBNStudy Guide and Intervention Workbook 0-07-660292-3 978-0-07-660292-6Homework Practice Workbook 0-07-660291-5 978-0-07-660291-9
Spanish VersionHomework Practice Workbook 0-07-660294-X 978-0-07-660294-0
Answers For Workbooks The answers for Chapter 5 of these workbooks can be found in the back of this Chapter Resource Masters booklet.
ConnectED All of the materials found in this booklet are included for viewing, printing, and editing at connected.mcgraw-hill.com.
Spanish Assessment Masters (MHID: 0-07-660289-3, ISBN: 978-0-07-660289-6) These masters contain a Spanish version of Chapter 5 Test Form 2A and Form 2C.
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Teacher’s Guide to Using the Chapter 5 Resource Masters .........................................iv
Chapter Resources Chapter 5 Student-Built Glossary ...................... 1Chapter 5 Anticipation Guide (English) ............. 3Chapter 5 Anticipation Guide (Spanish) ............ 4
Lesson 5-1Solving Inequalities by Addition and SubtractionStudy Guide and Intervention ............................ 5Skills Practice .................................................... 7Practice .............................................................. 8Word Problem Practice ...................................... 9Enrichment ...................................................... 10
Lesson 5-2Solving Inequalities by Multiplication and DivisionStudy Guide and Intervention ...........................11Skills Practice .................................................. 13Practice ........................................................... 14Word Problem Practice .................................... 15Enrichment ...................................................... 16
Lesson 5-3Solving Multi-Step InequalitiesStudy Guide and Intervention .......................... 17Skills Practice .................................................. 19Practice ........................................................... 20Word Problem Practice .................................... 21Enrichment ...................................................... 22
Lesson 5-4Solving Compound InequalitiesStudy Guide and Intervention .......................... 23Skills Practice .................................................. 25Practice ........................................................... 26Word Problem Practice .................................... 27Enrichment ...................................................... 28
Lesson 5-5Inequalities Involving Absolute ValueStudy Guide and Intervention .......................... 29Skills Practice .................................................. 31Practice ........................................................... 32Word Problem Practice .................................... 33Enrichment ...................................................... 34Graphing Calculator Activity ............................ 35
Lesson 5-6Graphing Inequalities in Two VariablesStudy Guide and Intervention .......................... 36Skills Practice .................................................. 38Practice ........................................................... 39Word Problem Practice .................................... 40Enrichment ...................................................... 41Spreadsheet Activity ........................................ 42
AssessmentStudent Recording Sheet ................................ 43Rubric for Scoring Extended Response .......... 44Chapter 5 Quizzes 1 and 2 ............................. 45Chapter 5 Quizzes 3 and 4 ............................. 46Chapter 5 Mid-Chapter Test ............................ 47Chapter 5 Vocabulary Test ............................... 48Chapter 5 Test, Form 1 .................................... 49Chapter 5 Test, Form 2A ................................. 51Chapter 5 Test, Form 2B ................................. 53Chapter 5 Test, Form 2C ................................. 55Chapter 5 Test, Form 2D ................................. 57Chapter 5 Test, Form 3 .................................... 59Chapter 5 Extended Response Test ................ 61Standardized Test Practice .............................. 62
Answers ........................................... A1–A31
Contents
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Teacher’s Guide to Using the Chapter 5 Resource Masters
The Chapter 5 Resource Masters includes the core materials needed for Chapter 5. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing, printing, and editing at connectED.mcgraw-hill.com.
Chapter ResourcesStudent-Built Glossary (pages 1–2) These masters are a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. Give this to students before beginning Lesson 5-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.
Anticipation Guide (pages 3–4) This master, presented in both English and Spanish, is a survey used before beginning the chapter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their perceptions have changed.
Lesson ResourcesStudy Guide and Intervention These masters provide vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteaching activity. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.
Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the lesson.
Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for second-day teaching of the lesson.
Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.
Enrichment These activities may extend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. They are written for use with all levels of students.
Graphing Calculator, TI-Nspire, or Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation.
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Assessment OptionsThe assessment masters in the Chapter 5 Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment.
Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter.
Extended Response This master provides information for teachers and students on how to assess performance on open-ended questions.
Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter.
Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 7 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.
Leveled Chapter Tests
• Form 1 contains multiple-choice questions and is intended for use with below grade level students.
• Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Form 3 is a free-response test for use with above grade level students.
All of the above mentioned tests include a free-response Bonus question.
Extended-Response Test Performance assessment tasks are suitable for all students. Sample answers and a scoring rubric are included for evaluation.
Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided as reduced pages with answers appearing in bold, black.
• Full-size answer keys are provided for the assessment masters.
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Chapter 5 1 Glencoe Algebra 1
Student-Built Glossary
This is an alphabetical list of the key vocabulary terms you will learn in Chapter 5. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary TermFound
on PageDefi nition/Description/Example
boundary
closed half-plane
compound inequality
half-plane
intersection
open half-plane
set-builder notation
union
5
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Chapter 5 3 Glencoe Algebra 1
Anticipation GuideLinear Inequalities
Before you begin Chapter 5
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).
STEP 1A, D, or NS
StatementSTEP 2A or D
1. According to the Addition Property of Inequalities, adding any number to each side of a true inequality will result in a true inequality.
2. The inequality m + 23 ≥ 35 can be solved by adding 23 to each side.
3. 16 is no greater than the difference of a number and 12 can be written as 16 ≤ n – 12.
4. If both sides of r − 12
< 4 are multiplied by 12, the result is r < 48.
5. The result of dividing both sides of the inequality –2y ≥ 10 by –2 is y ≥ –5.
6. To solve an inequality involving multiplication, such as 9t > 27, division is used.
7. To solve the inequality 8x – 2 < 70, first divide by 8 and then add 2.
8. A compound inequality is an inequality containing more than one variable.
9. On a number line, a closed dot is used for an inequality containing the symbol ≥ or ≤.
10. If ⎪t⎥ < 8, then t equals all numbers between 0 and 8.11. On the graph of y > 2x – 3, the solution set will be all
numbers above the graph of the line y = 2x – 3.
After you complete Chapter 5
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.
Step 1
5
Step 2
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PDF 2nd
Capítulo 5 4 Álgebra 1 de Glencoe
Antes de comenzar el Capítulo 5
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a)).
PASO 1A, D o NS
EnunciadoPASO 2A o D
1. Según la propiedad de adición de la desigualdad, sumar cualquier número a cada lado de una desigualdad verdadera dará como resultado una desigualdad verdadera.
2. La desigualdad m + 23 ≥ 35 se puede resolver al sumar 23 a cada lado.
3. 16 no es más que la diferencia entre un número y 12 se puede escribir como 16 ≤ n – 12.
4. Si ambos lados de r − 12
< 4 se multiplican por 12, el resultado es r < 48.
5. El resultado de dividir ambos lados de la desigualdad –2y ≥ 10 entre –2 es y ≥ –5.
6. Para resolver una desigualdad que implica multiplicación, como 9t > 27, se usa la división.
7. Para resolver la desigualdad 8x – 2 < 70, primero divide entre 8 y luego suma 2.
8. Una desigualdad compuesta es una desigualdad que contiene más de una variable.
9. En una recta numérica, un punto cerrado se usa para una desigualdad con el símbolo ≥ o ≤.
10. Si ⎪t⎥ < 8, entonces t igual a todos los números entre 0 y 8.
11. En la gráfica de y > 2x – 3, el conjunto solución será el de todos los números arriba de la gráfica de la recta y = 2x – 3.
Después de completar el Capítulo 5
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D.
Paso 1
Paso 2
5 Ejercicios preparatoriosDesigualdades lineales
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Chapter 5 5 Glencoe Algebra 1
Study Guide and InterventionSolving Inequalities by Addition and Subtraction
Solve Inequalities by Addition Addition can be used to solve inequalities. If any number is added to each side of a true inequality, the resulting inequality is also true.
Addition Property of Inequalities For all numbers a, b, and c, if a > b, then a + c > b + c, and if a < b, then a + c < b + c.
The property is also true when > and < are replaced with ≥ and ≤.
Solve x - 8 ≤ -6. Then graph the solution. x - 8 ≤ -6 Original inequality
x - 8 + 8 ≤ -6 + 8 Add 8 to each side.
x ≤ 2 Simplify.
The solution in set-builder notation is {x|x ≤ 2}.Number line graph:
-4 -3 -2 -1 0 1 2 3 4
Solve 4 - 2a > -a. Then graph the solution. 4 - 2a > -a Original inequality
4 - 2a + 2a > -a + 2a Add 2a to each side.
4 > a Simplify.
a < 4 4 > a is the same as a < 4.
The solution in set-builder notation is {a|a < 4}.Number line graph:
-2 -1 0 1 2 3 4 5 6
ExercisesSolve each inequality. Check your solution, and then graph it on a number line.
1. t - 12 ≥ 16 2. n - 12 < 6 3. 6 ≤ g - 3
26 27 28 29 30 31 32 33 34
14 1512 13 16 17 18 19 20
7 8 9 10 11 12 13 14 15
4. n - 8 < -13 5. -12 > -12 + y 6. -6 > m - 8
-9-10 -8 -7 -6 -5 -4 -3 -2
-3-4 -2 -1 0 1 2 3 4
-4 -2 -1 0 1 2 3-3 4
Solve each inequality. Check your solution.
7. -3x ≤ 8 - 4x 8. 0.6n ≥ 12 - 0.4n 9. -8k - 12 < - 9k
10. -y - 10 > 15 - 2y 11. z - 1 − 3 ≤ 4 −
3 12. -2b > -4 - 3b
Define a variable, write an inequality, and solve each problem. Check your solution.
13. A number decreased by 4 is less than 14.
14. The difference of two numbers is more than 12, and one of the numbers is 3.
15. Forty is no greater than the difference of a number and 2.
5-1
Example 1 Example 2
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Chapter 5 6 Glencoe Algebra 1
Study Guide and Intervention (continued)
Solving Inequalities by Addition and Subtraction
Solve Inequalities by Subtraction Subtraction can be used to solve inequalities. If any number is subtracted from each side of a true inequality, the resulting inequality is also true.
Subtraction Property of InequalitiesFor all numbers a, b, and c, if a > b, then a - c > b - c, and if a < b, then a - c < b - c.
The property is also true when > and < are replaced with ≥ and ≤.
Solve 3a + 5 > 4 + 2a. Then graph it on a number line.
3a + 5 > 4 + 2a Original inequality
3a + 5 - 2a > 4 + 2a - 2a Subtract 2a from each side.
a + 5 > 4 Simplify.
a + 5 - 5 > 4 - 5 Subtract 5 from each side.
a > -1 Simplify.
The solution is {a�a > -1}.Number line graph:
-4 -3 -2 -1 0 1 2 3 4
ExercisesSolve each inequality. Check your solution, and then graph it on a number line. 1. t + 12 ≥ 8 2. n + 12 > -12 3. 16 ≤ h + 9
-6 -5 -4 -3 -2 -1 0 1 2
-26 -25 -24 -23 -22 -21 5 6 7 8 9 10 11 12 13
4. y + 4 > - 2 5. 3r + 6 > 4r 6. 3 − 2 q - 5 ≥ 1 −
2 q
-8 -7 -6 -5 -4 -3 -2 -1 0
2 3 4 5 6 7 91 8
210 3 4 5 6 7 8
Solve each inequality. Check your solution. 7. 4p ≥ 3p + 0.7 8. r + 1 −
4 > 3 −
8 9. 9k + 12 > 8k
10. -1.2 > 2.4 + y 11. 4y < 5y+ 14 12. 3n + 17 < 4n
Define a variable, write an inequality, and solve each problem. Check your solution.
13. The sum of a number and 8 is less than 12.
14. The sum of two numbers is at most 6, and one of the numbers is -2.
15. The sum of a number and 6 is greater than or equal to -4.
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Chapter 5 7 Glencoe Algebra 1
Skills PracticeSolving Inequalities by Addition and Subtraction
Match each inequality to the graph of its solution.
1. x + 11 > 16 a. -8 -7 -6 -5 -4 -3 -2 -1 0
2. x - 6 < 1 b.
3. x + 2 ≤ -3 c.
4. x + 3 ≥ 1 d.
5. x - 1 < -7 e.
Solve each inequality. Check your solution, and then graph it on a number line.
6. d - 5 ≤ 1 7. t + 9 < 8
2 30 1 4 5 6 7 8
-2 -1-4 -3 0 1 2 3 4
8. a - 7 > -13 9. w - 1 < 4
-8 -7 -6 -5 -4 -3 -2 -1 0
2 30 1 4 5 6 7 8
10. 4 ≥ k + 3 11. -9 ≤ b - 4
-2 -1-4 -3 0 1 2 3 4
-8 -7 -6 -5 -4 -3 -2 -1 0
12. -2 ≥ x + 4 13. 2y < y + 2
-6 -5-8 -7 -4 -3 -2 -1 0
-2 -1-4 -3 0 1 2 3 4
Define a variable, write an inequality, and solve each problem. Check your solution.
14. A number decreased by 10 is greater than -5.
15. A number increased by 1 is less than 9.
16. Seven more than a number is less than or equal to -18.
17. Twenty less than a number is at least 15.
18. A number plus 2 is at most 1.
-8 -7 -6 -5 -4 -3 -2 -1 0
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Chapter 5 8 Glencoe Algebra 1
5-1
Match each inequality with its corresponding graph.
1. -8 ≥ x - 15 a. -6 -5 -4 -3 -2 -1 0 1 2
2. 4x + 3 < 5x b. 876543210
3. 8x > 7x - 4 c. -8 -7 -6 -5 -4 -3 -2 -1 0
4. 12 + x ≤ 9 d. 2 3 4 5 6 7 810
Solve each inequality. Check your solution, and then graph it on a number line.
5. r - (-5) > -2 6. 3x + 8 ≥ 4x
-8 -7 -6 -5 -4 -3 -2 -1 0
4 52 3 6 7 8 9 10
7. n - 2.5 ≥ -5 8. 1.5 < y + 1
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4
9. z + 3 > 2 − 3 10. 1 −
2 ≤ c - 3 −
4
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4
Define a variable, write an inequality, and solve each problem. Check your solution.
11. The sum of a number and 17 is no less than 26.
12. Twice a number minus 4 is less than three times the number.
13. Twelve is at most a number decreased by 7.
14. Eight plus four times a number is greater than five times the number.
15. ATMOSPHERIC SCIENCE The troposphere extends from the Earth’s surface to a height of 6–12 miles, depending on the location and the season. If a plane is flying at an altitude of 5.8 miles, and the troposphere is 8.6 miles deep in that area, how much higher can the plane go without leaving the troposphere?
16. EARTH SCIENCE Mature soil is composed of three layers, the uppermost being topsoil. Jamal is planting a bush that needs a hole 18 centimeters deep for the roots. The instructions suggest an additional 8 centimeters depth for a cushion. If Jamal wants to add even more cushion, and the topsoil in his yard is 30 centimeters deep, how much more cushion can he add and still remain in the topsoil layer?
PracticeSolving Inequalities by Addition and Subtraction
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Chapter 5 9 Glencoe Algebra 1
Word Problem PracticeSolving Inequalities by Addition and Subtraction
1. SOUND The loudest insect on Earth is the African cicada. It produces sounds as loud as 105 decibels at 20 inches away. The blue whale is the loudest mammal on Earth. The call of the blue whale can reach levels up to 83 decibels louder than the African cicada. How loud are the calls of the blue whale?
2. GARBAGE The amount of garbage that the average American adds to a landfill daily is 4.6 pounds. If at least 2.5 pounds of a person’s daily garbage could be recycled, how much will still go into a landfill?
3. SHOPPING Tyler has $75 to spend at the mall. He purchases a music video for $14.99 and a pair of jeans for $18.99. He also spent $4.75 for lunch. Tyler still wants to purchase a video game. How much money can he spend on a video game?
4. SUPREME COURT The first Chief Justice of the U.S. Supreme Court, John Jay, served 2079 days as Chief Justice. He served 10,463 days fewer than John Marshall, who served as Supreme Court Chief Justice for the longest period of time. How many days must the current Supreme Court Chief Justice John Roberts serve to surpass John Marshall’s record of service?
5. WEATHER Theodore Fujita of the University of Chicago developed a classification of tornadoes according to wind speed and damage. The table shows the classification system.
Level NameWind Speed Range
(mph)
F0 Gale 40 –72
F1 Moderate 73–112
F2 Signifi cant 113–157
F3 Severe 158–206
F4 Devastating 207–260
F5 Incredible 261–318
F6 Inconceivable 319–379
Source: National Weather Service
a. Suppose an F3 tornado has winds that are 162 miles per hour. Write and solve an inequality to determine how much the winds would have to increase before the F3 tornado becomes an F4 tornado.
b. A tornado has wind speeds that are at least 158 miles per hour. Write and solve an inequality that describes how much greater these wind speeds are than the slowest tornado.
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Chapter 5 10 Glencoe Algebra 1
Enrichment
Triangle InequalitiesRecall that a line segment can be named by the letters of its endpoints. Line segment AB (written as
−− AB ) has points A and B for
endpoints. The length of AB is written without the bar as AB.
AB > BC m∠ A < m∠ B
The statement on the left above shows that −−
AB is shorter than −−−
BC . The statement on the right above shows that the measure of angle A is less than that of angle B.
These three inequalities are true for any triangle ABC, no matter how long the sides.
a. AB + BC > ACb. If AB > AC, then m∠C > m∠B.c. If m∠C > m∠B, then AB > AC.
B
A C
Use the three triangle inequalities for these problems.
1. List the sides of triangle DEF in order of increasing length. D
F E60° 35°
85°
2. In the figure at the right, which line segment is the shortest?
JM
K
L
65°
60°65°55°
65°50°
3. Explain why the lengths 5 centimeters, 10 centimeters, and 20 centimeters could not be used to make a triangle.
4. Two sides of a triangle measure 3 inches and 7 inches. Between which two values must the third side be?
5. In triangle XYZ, XY = 15, YZ = 12, and XZ = 9. Which angle has the greatest measure? Which has the least?
6. List the angles ∠A, ∠C, ∠ABC, and ∠ABD, in order of increasing size. C
A
DB
13
15
12
5
9
5-1
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Chapter 5 11 Glencoe Algebra 1
Study Guide and InterventionSolving Inequalities by Multiplication and Division
Solve Inequalities by Multiplication If each side of an inequality is multiplied by the same positive number, the resulting inequality is also true. However, if each side of an inequality is multiplied by the same negative number, the direction of the inequality must be reversed for the resulting inequality to be true.
Multiplication Property of Inequalities
For all numbers a, b, and c, with c ≠ 0,
1. if c is positive and a > b, then ac > bc;
if c is positive and a < b, then ac < bc;
2. if c is negative and a > b, then ac < bc;
if c is negative and a < b, then ac > bc.
The property is also true when > and < are replaced with ≥ and ≤.
Solve - y −
8 ≤ 12.
- y −
8 ≥ 12 Original inequality
(-8) (-
y −
8 ) ≤ (-8)12 Multiply each side by -8; change ≥ to ≤.
y ≤ -96 Simplify.
The solution is { y � y ≤ -96}.
Solve 3 −
4 k < 15.
3 − 4 k < 15 Original inequality
( 4 − 3 ) 3 −
4 k < ( 4 −
3 ) 15 Multiply each side by 4 −
3 .
k < 20 Simplify.
The solution is {k � k < 20}.
ExercisesSolve each inequality. Check your solution.
1. y −
6 ≤ 2 2. -
n − 50
> 22 3. 3 − 5 h ≥ -3 4. -
p −
6 < -6
5. 1 − 4 n ≥ 10 6. -
2 − 3 b < 1 −
3 7. 3m −
5 < -
3 − 20
8. -2.51 ≤ - 2h − 4
9. g −
5 ≥ -2 10. - 3 −
4 > -
9p −
5 11. n −
10 ≥ 5.4 12. 2a −
7 ≥ -6
Define a variable, write an inequality, and solve each problem. Check your solution.
13. Half of a number is at least 14.
14. The opposite of one-third a number is greater than 9.
15. One fifth of a number is at most 30.
5-2
Example 1 Example 2
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Chapter 5 12 Glencoe Algebra 1
Study Guide and Intervention (continued)
Solving Inequalities by Multiplication and Division
Solve Inequalities by Division If each side of a true inequality is divided by the same positive number, the resulting inequality is also true. However, if each side of an inequality is divided by the same negative number, the direction of the inequality symbol must be reversed for the resulting inequality to be true.
Division Property of Inequalities
For all numbers a, b, and c with c ≠ 0,
1. if c is positive and a > b, then a − c > b − c ; if c is positive and a < b, then a − c < b − c ;
2. if c is negative and a > b, then a − c < b − c ; if c is negative and a < b, then a − c > b − c .
The property is also true when > and < are replaced with ≥ and ≤.
Solve -12y ≥ 48.
-12y ≥ 48 Original inequality
-12y
− -12
≤ 48 − -12
Divide each side by -12 and change ≥ to ≤.
y ≤ -4 Simplify.
The solution is { y �
y ≤ -4}.
ExercisesSolve each inequality. Check your solution.
1. 25g ≥ -100 2. -2x ≥ 9 3. -5c > 2 4. -8m < -64
5. -6k < 1 − 5 6. 18 < -3b 7. 30 < -3n 8. -0.24 < 0.6w
9. 25 ≥ -2m 10. -30 > -5p 11. -2n ≥ 6.2 12. 35 < 0.05h
13. -40 > 10h 14. - 2 −
3n ≥ 6 15. -3 <
p −
4 16. 4 > -x −
2
Define a variable, write an inequality, and solve each problem. Then check your solution.
17. Four times a number is no more than 108.
18. The opposite of three times a number is greater than 12.
19. Negative five times a number is at most 100.
5-2
Example
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Chapter 5 13 Glencoe Algebra 1
Skills PracticeSolving Inequalities by Multiplication and Division
Match each inequality with its corresponding statement.
1. 3n < 9 a. Three times a number is at most nine.
2. 1 − 3 n ≥ 9 b. One third of a number is no more than nine.
3. 3n ≤ 9 c. Negative three times a number is more than nine.
4. -3n > 9 d. Three times a number is less than nine.
5. 1 − 3 n ≤ 9 e. Negative three times a number is at least nine.
6. -3n ≥ 9 f. One third of a number is greater than or equal to nine.
Solve each inequality. Check your solution.
7. 14g > 56 8. 11w ≤ 77 9. 20b ≥ -120 10. -8r < 16
11. -15p ≤ -90 12. x − 4 < 9 13. a −
9 ≥ -15 14. -
p −
7 > -9
15. - t −
12 ≥ 6 16. 5z < -90 17. -13m > -26 18. k −
5 ≤ -17
19. -y < 36 20. -16c ≥ -224 21. - h − 10
≤ 2 22. 12 > d − 12
Define a variable, write an inequality, and solve each problem. Check your solution.
23. Four times a number is greater than -48.
24. One eighth of a number is less than or equal to 3.
25. Negative twelve times a number is no more than 84.
26. Negative one sixth of a number is less than -9.
27. Eight times a number is at least 16.
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Chapter 5 14 Glencoe Algebra 1
Match each inequality with its corresponding statement.
1. -4n ≥ 5 a. Negative four times a number is less than five.
2. 4 − 5 n > 5 b. Four fifths of a number is no more than five.
3. 4n ≤ 5 c. Four times a number is fewer than five.
4. 4 − 5 n ≤ 5 d. Negative four times a number is no less than five.
5. 4n < 5 e. Four times a number is at most five.
6. -4n < 5 f. Four fifths of a number is more than five.
Solve each inequality. Check your solution.
7. - a − 5
< -14 8. -13h ≤ 52 9. b − 16
≥ -6 10. 39 > 13p
11. 2 − 3 n > -12 12. -
5 − 9 t < 25 13. -
3 − 5 m ≤ -6 14. 10 −
3 k ≥ -10
15. -3b ≤ 0.75 16. -0.9c > -9 17. 0.1x ≥ -4 18. -2.3 < j −
4
19. -15y < 3 20. 2.6v ≥ -20.8 21. 0 > -0.5u 22. 7 − 8 f ≤ -1
Define a variable, write an inequality, and solve each problem. Check your solution.
23. Negative three times a number is at least 57.
24. Two thirds of a number is no more than -10.
25. Negative three fifths of a number is less than -6.
26. FLOODING A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage?
27. SALES Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225 on natural dog food, how many bags of dog food does it need to sell?
5-2 PracticeSolving Inequalities by Multiplication and Division
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Chapter 5 15 Glencoe Algebra 1
1. PIZZA Tara and friends order a pizza. Tara eats 3 of the 10 slices and pays $4.20 for her share. Assuming that Tara has paid at least her fair share, write an ineqality for how much the pizza could have cost.
2. AIRLINES On average, at least 25,000 pieces of luggage are lost or misdirected each day by United States airlines. Of these, 98% are located by the airlines within 5 days. From a given day’s lost luggage, at least how many pieces of luggage are still lost after 5 days?
3. SCHOOL Gil earned these scores on the first three tests in biology this term: 86, 88, and 78. What is the lowest score that Gil can earn on the fourth and final test of the term if he wants to have an average of at least 83?
4. EVENT PLANNING The Downtown Community Center does not charge a rental fee as long as a rentee orders a minimum of $5000 worth of food from the center. Antonio is planning a banquet for the Quarterback Club. If he is expecting 225 people to attend, what is the minimum he will have to spend on food per person to avoid paying a rental fee?
5. PHYSICS The density of a substance determines whether it will float or sink in a liquid. The density of water is 1 gram per milliliter. Any object with a greater density will sink and any object with a lesser density will float. Density is given by the formula d =
m − v , where m is mass and v is volume. Here is a table of common chemical solutions and their densities.
Solution Density (g/mL)
concentrated calcium chloride 1.40
70% isopropyl alcohol 0.92
Source: American Chemistry Council
a. Plastics vary in density when they are manufactured; therefore, their volumes are variable for a given mass. A tablet of polystyrene (a manufactured plastic) sinks in water and in alcohol solution and floats in calcium chloride solution. The tablet has a mass of 0.4 gram. What is the most its volume can be?
b. What is the least its volume can be?
Word Problem PracticeSolving Inequalities by Multiplication and Division
5-2
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Chapter 5 16 Glencoe Algebra 1
Enrichment
Quadratic InequalitiesLike linear inequalities, inequalities with higher degrees can also be solved. Quadratic inequalities have a degree of 2. The following example shows how to solve quadratic inequalities.
Solve (x + 3)(x - 2) > 0.
Step 1 Determine what values of x will make the left side 0. In other words, what values of x will make either x + 3 = 0 or x - 2 = 0?
x = -3 or 2
Step 2 Plot these points on a number line. Above the number line, place a + if x + 3 is positive for that region or a - if x + 3 is negative for that region. Next, above the signs you have just entered; do the same for x – 2.
Step 3 Below the chart, enter the product of the two signs. Your sign chart should look like the following:
5 6-6 43210-1-5-4-3-2
x - 2
x + 3
(x - 2)(x + 3)
The final positive regions correspond to values for which the quadratic expression is greater than 0. So, the answer is
x < -3 or x > 2.
ExercisesSolve each inequality.
1. (x - 1)(x + 2) > 0 2. (x + 5)(x + 2) > 0
3. (x - 1)(x - 5) < 0 4. (x + 2)(x - 4) ≤ 0
5. (x – 3)(x + 2) ≥ 0 6. (x + 3)(x - 4) ≤ 0
5-2
Example
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Chapter 5 17 Glencoe Algebra 1
Study Guide and InterventionSolving Multi-Step Inequalities
Solve Multi-Step Inequalities To solve linear inequalities involving more than one operation, undo the operations in reverse of the order of operations, just as you would solve an equation with more than one operation.
Solve 6x - 4 ≤ 2x + 12.6x - 4 ≤ 2x + 12 Original inequality
6x - 4 - 2x ≤ 2x + 12 - 2x Subtract 2x from
each side.
4x - 4 ≤ 12 Simplify.
4x - 4 + 4 ≤ 12 + 4 Add 4 to each side.
4x ≤ 16 Simplify.
4x − 4 ≤
16 −
4 Divide each side by 4.
x ≤ 4 Simplify.
The solution is {x � x ≤ 4}.
Solve 3a - 15 > 4 + 5a.
3a - 15 > 4 + 5a Original inequality
3a - 15 - 5a > 4 + 5a - 5a Subtract 5a from
each side.
-2a - 15 > 4 Simplify.
-2a - 15 + 15 > 4 + 15 Add 15 to each side.
-2a > 19 Simplify.
-2a − -2
< 19 − -2
Divide each side by -2
and change > to <.
a < -9 1 − 2 Simplify.
The solution is {a � a < -9 1 − 2 } .
ExercisesSolve each inequality. Check your solution.
1. 11y + 13 ≥ -1 2. 8n - 10 < 6 - 2n 3. q −
7 + 1 > -5
4. 6n + 12 < 8 + 8n 5. -12 - d > -12 + 4d 6. 5r - 6 > 8r - 18
7. -3x + 6 − 2 ≤ 12 8. 7.3y - 14.4 > 4.9y 9. -8m - 3 < 18 - m
10. -4y - 10 > 19 - 2y 11. 9n - 24n + 45 > 0 12. 4x - 2 − 5 ≥ -4
Define a variable, write an inequality, and solve each problem. Check your solution.
13. Negative three times a number plus four is no more than the number minus eight.
14. One fourth of a number decreased by three is at least two.
15. The sum of twelve and a number is no greater than the sum of twice the number and -8.
5-3
Example 1 Example 2
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Chapter 5 18 Glencoe Algebra 1
Study Guide and Intervention (continued)
Solving Multi-Step Inequalities
Solve Inequalities Involving the Distributive Property When solving inequalities that contain grouping symbols, first use the Distributive Property to remove the grouping symbols. Then undo the operations in reverse of the order of operations, just as you would solve an equation with more than one operation.
Solve 3a - 2(6a - 4) > 4 - (4a + 6).
3a - 2(6a - 4) > 4 - (4a + 6) Original inequality
3a - 12a + 8 > 4 - 4a - 6 Distributive Property
-9a + 8 > -2 - 4a Combine like terms.
-9a + 8 + 4a > -2 - 4a + 4a Add 4a to each side.
-5a + 8 > -2 Combine like terms.
-5a + 8 - 8 > -2 - 8 Subtract 8 from each side.
-5a > -10 Simplify.
a < 2 Divide each side by -5 and change > to <.
The solution in set-builder notation is {a � a < 2}.
ExercisesSolve each inequality. Check your solution.
1. 2(t + 3) ≥ 16 2. 3(d - 2) - 2d > 16 3. 4h - 8 < 2(h - 1)
4. 6y + 10 > 8 - (y + 14) 5. 4.6(x - 3.4) > 5.1x 6. -5x - (2x + 3) ≥ 1
7. 3(2y - 4) - 2(y + 1) > 10 8. 8 - 2(b + 1) < 12 - 3b 9. -2(k - 1) > 8(1+ k)
10. 0.3( y - 2) > 0.4(1 + y) 11. m + 17 ≤ -(4m - 13)
12. 3n + 8 ≤ 2(n - 4) - 2(1 - n) 13. 2(y - 2) > -4 + 2y
14. k - 17 ≤ -(17 - k) 15. n - 4 ≤ - 3(2 + n)
Define a variable, write an inequality, and solve each problem. Check your solution.
16. Twice the sum of a number and 4 is less than 12.
17. Three times the sum of a number and six is greater than four times the number decreased by two.
18. Twice the difference of a number and four is less than the sum of the number and five.
5-3
Example
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Chapter 5 19 Glencoe Algebra 1
Skills PracticeSolving Multi-Step Inequalities
Justify each indicated step.
1. 3 − 4 t - 3 ≥ -15
3 − 4 t - 3 + 3 ≥ -15 + 3 a. ?
3 − 4 t ≥ -12
4 − 3 (
3 − 4 ) t ≥ 4 −
3 (-12) b. ?
t ≥ -16
2. 5(k + 8) - 7 ≤ 23 5k + 40 - 7 ≤ 23 a. ?
5k + 33 ≤ 235k + 33 - 33 ≤ 23 - 33 b. ?
5k ≤ -10 5k − 5 ≤ -10 −
5 c. ?
k ≤ -2
Solve each inequality. Check your solution.
3. -2b + 4 > -6 4. 3x + 15 ≤ 21 5. d − 2 - 1 ≥ 3
6. 2 − 5 a - 4 < 2 7. -
t − 5 + 7 > -4 8. 3 −
4 j - 10 ≥ 5
9. - 2 − 3 f + 3 < -9 10. 2p + 5 ≥ 3p - 10 11. 4k + 15 > -2k + 3
12. 2(-3m - 5) ≥ -28 13. -6(w + 1) < 2(w + 5) 14. 2(q - 3) + 6 ≤ -10
Define a variable, write an inequality, and solve each problem. Check your solution.
15. Four more than the quotient of a number and three is at least nine.
16. The sum of a number and fourteen is less than or equal to three times the number.
17. Negative three times a number increased by seven is less than negative eleven.
18. Five times a number decreased by eight is at most ten more than twice the number.
19. Seven more than five sixths of a number is more than negative three.
20. Four times the sum of a number and two increased by three is at least twenty-seven.
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Chapter 5 20 Glencoe Algebra 1
PracticeSolving Multi-Step Inequalities
Justify each indicated step. 1. x > 5x - 12 −
8
8x > (8) 5x - 12 − 8 a. ?
8x > 5x - 12
8x - 5x > 5x - 12 - 5x b. ?
3x > -12
3x − 3 > -12 −
3 c. ?
x > -4
2. 2(2h + 2) < 2(3h + 5) - 124h + 4 < 6h + 10 - 12 a. ?4h + 4 < 6h - 2
4h + 4 - 6h < 6h - 2 - 6h b. ?-2h + 4 < -2
-2h + 4 - 4 < -2 - 4 c. ?-2h < -6
-2h − -2
> -6 − -2
d. ?
h > 3
Solve each inequality. Check your solution.
3. -5 - t − 6 ≥ -9 4. 4u - 6 ≥ 6u - 20 5. 13 > 2 −
3 a - 1
6. w + 3 − 2 < -8 7.
3f - 10 −
5 > 7
8. h ≤ 6h + 3 −
5 9. 3(z + 1) + 11 < -2(z + 13)
10. 3r + 2(4r + 2) ≤ 2(6r + 1) 11. 5n - 3(n - 6) ≥ 0
Define a variable, write an inequality, and solve each problem. Check your solution.
12. A number is less than one fourth the sum of three times the number and four.
13. Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four.
14. GEOMETRY The area of a triangular garden can be no more than 120 square feet. The base of the triangle is 16 feet. What is the height of the triangle?
15. MUSIC PRACTICE Nabuko practices the violin at least 12 hours per week. She practices for three fourths of an hour each session. If Nabuko has already practiced 3 hours in one week, how many sessions remain to meet or exceed her weekly practice goal?
5-3
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Chapter 5 21 Glencoe Algebra 1
Word Problem PracticeSolving Multi-Step Inequalities
1. BEACHCOMBING Jay has lost his mother’s favorite necklace, so he will rent a metal detector to try to find it. A rental company charges a one-time rental fee of $15 plus $2 per hour to rent a metal detector. Jay has only $35 to spend. What is the maximum amount of time he can rent the metal detector?
2. AGES Bobby, Billy, and Barry Smith are each one year apart in age. The sum of their ages is greater than the age of their father, who is 60. How old can the oldest brother can be?
3. TAXI FARE Jamal works in a city and sometimes takes a taxi to work. The taxicabs charge $1.50 for the first 1−
5 mile
and $0.25 for each additional 1−5
mile.
Jamal has only $3.75 in his pocket. What is the maximum distance he can travel by taxi if he does not tip the driver?
4. PLAYGROUND The perimeter of a rectangular playground must be no greater than 120 meters, because that is the total length of the materials available for the border. The width of the playground cannot exceed 22 meters. What are the possible lengths of the playground?
5. MEDICINE Clark’s Rule is a formula used to determine pediatric dosages of over-the-counter medicines.
weight of child ( lb) −
150 × adult dose = child
dose
a. If an adult dose of acetaminophen is 1000 milligrams and a child weighs no more than 90 pounds, what is the recommended child’s dose?
b. This label appears on a child’s cold medicine. What is the adult minimum dosage in milliliters?
Weight (lb) Age (yr) Dose
under 48 under 6 call a doctor
48-95 6-11 2 tsp or 10 mL
c. What is the maximum adult dosage in milliliters?
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Chapter 5 22 Glencoe Algebra 1
Enrichment
Carlos Montezuma During his lifetime, Carlos Montezuma (1866–1923) was one of the most influential Native Americans in the United States. He was recognized as a prominent physician and was also a passionate advocate of the rights of Native American peoples. The exercises that follow will help you learn some interesting facts about Dr. Montezuma’s life.
Solve each inequality. The word or phrase next to the equivalent inequality will complete the statement correctly.
1. -2k > 10 2. 5 ≥ r - 9 Montezuma was born in the state He was a Native American of the
of ? . Yavapais, who are a ? people.
a. k < -5 Arizona a. r ≤ -4 Navajo
b. k > -5 Montana b. r ≥ -4 Mohawk
c. k > 12 Utah c. r ≤ 14 Mohave-Apache
3. -y ≤ -9 4. -3 + q > 12 Montezuma received a medical As a physician, Montezuma’s field of
degree from ? in 1889. specialization was ? .
a. y ≥ 9 Chicago Medical College a. q > -4 heart surgery
b. y ≥ -9 Harvard Medical School b. q > 15 internal medicine
c. y ≤ 9 Johns Hopkins University c. q < -15 respiratory diseases
5. 5 + 4x - 14 ≤ x 6. 7 - t < 7 + t For much of his career, he maintained In addition to maintaining his medical
a medical practice in ? . practice, he was also a(n) ? .
a. x ≤ 9 New York City a. t > 7 director of a blood bank
b. x ≤ 3 Chicago b. t > 0 instructor at a medical college
c. x ≥ -9 Boston c. t < -7 legal counsel to physicians
7. 3a + 8 ≥ 4a - 10 8. 6n > 8n - 12 Montezuma founded, wrote, and Montezuma testified before a
edited ? , a monthly newsletter committee of the United States that addressed Native American Congress concerning his work in concerns. treating ? .
a. a ≤ -2 Yavapai a. n < 6 appendicitis
b. a ≥ 18 Apache b. n > -6 asthma
c. a ≤ 18 Wassaja c. n > -10 heart attacks
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Study Guide and InterventionSolving Compound Inequalities
Inequalities Containing and A compound inequality containing and is true only if both inequalities are true. The graph of a compound inequality containing and is the intersection of the graphs of the two inequalities. Every solution of the compound inequality must be a solution of both inequalities.
Graph the solution set of x < 2 and x ≥ -1. Graph x < 2.
Graph x ≥ -1.
Find the intersection.
The solution set is {x � -1 ≤ x < 2}.
Solve -1 < x + 2 < 3. Then graph the solution set.
-1 < x + 2 and x + 2 < 3-1 - 2 < x + 2 - 2 x + 2 - 2 < 3 - 2
-3 < x x < 1
Graph x > -3.
Graph x < 1.
Find the intersection.
The solution set is {x � -3 < x < 1}.
ExercisesGraph the solution set of each compound inequality.
1. b > -1 and b ≤ 3 2. 2 ≥ q ≥ -5 3. x > -3 and x ≤ 4
4. -2 ≤ p < 4 5. -3 < d and d< 2 6. -1 ≤ p ≤ 3
Solve each compound inequality. Then graph the solution set.
7. 4 < w + 3 ≤ 5 8. -3 ≤ p - 5 < 2
9. -4 < x + 2 ≤ -2 10. y - 1 < 2 and y + 2 ≥ 1
11. n - 2 > -3 and n + 4 < 6 12. d - 3 < 6d + 12 < 2d + 32
-2 -1-3 0 1 2 3
-3 -2 -1 0 1 2 3
-3 -2 -1 0 1 2 3
-3 -2 -1 0 1 2 3 4 5-3-4 -2 -1 0 1 2 3 4
-3-4 -2 -1 0 1 2 3 4-7 -6 -5 -4 -3 -2 -1 0 1
0 1 2 3 4 5 6 7 8-3-4 -2 -1 0 1 2 3 4
-3-4 -2 -1 0 1 2 3 4-3-4 -2 -1 0 1 2 3 4-3 -2 -1 0 1 2 3 4 5
-4 -3 -2 -1 0 1 2 3 4-4 -3-6 -5 -2 -1 0 1 2-4 -3 -2 -1 0 1 2 3 4
-2 -1-4 -3 0 1 2
-3-4 -2 -1 0 1 2
-3-4 -2 -1 0 1 2
5-4
Chapter 5 23 Glencoe Algebra 1
Example 1 Example 2
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Chapter 5 24 Glencoe Algebra 1
Study Guide and Intervention (continued)
Solving Compound Inequalities
Inequalities Containing or A compound inequality containing or is true if one or both of the inequalities are true. The graph of a compound inequality containing or is the union of the graphs of the two inequalities. The union can be found by graphing both inequalities on the same number line. A solution of the compound inequality is a solution of either inequality, not necessarily both.
Solve 2a + 1 < 11 or a > 3a + 2. Then graph the solution set.
2a + 1 < 11 or a > 3a + 2 2a + 1 - 1 < 11 - 1 a - 3a > 3a - 3a + 2 2a < 10 -2a > 2
2a −
2 < 10 −
2
-2a − -2
< 2 − -2
a < 5 a < -1
-2 -1 0 1 2 3 4 5 6 Graph a < 5.
-2 -1 0 1 2 3 4 5 6 Graph a < -1.
-2 -1 0 1 2 3 4 5 6 Find the union.
The solution set is {a � a < 5}.
ExercisesGraph the solution set of each compound inequality. 1. b > 2 or b ≤ -3 2. 3 ≥ q or q ≤ 1 3. y ≤ -4 or y > 0
4. 4 ≤ p or p < 8 5. -3 < d or d < 2 6. -2 ≤ x or 3 ≤ x
Solve each compound inequality. Then graph the solution set.
7. 3 < 3w or 3w ≥ 9 8. -3p + 1 ≤ -11 or p < 2
9. 2x + 4 ≤ 6 or x ≥ 2x - 4 10. 2y + 2 < 12 or y - 3 ≥ 2y
11. 1 − 2 n > -2 or 2n - 2 < 6 + n 12. 3a + 2 ≥ 5 or 7 + 3a < 2a + 6
0-1-2-3-4 1 2 3 40-1-2-3-4 1 2 3 4
0 1 2 3 4 5 6 7 8-2 -1 0 1 2 3 4 5 6
0 1 2 3 4 5 6 7 8-3-4 -2 -1 0 1 2 3 4
-3-4 -2 -1 0 1 2 3 40-1-2-3-4 1 2 3 40-1-2 1 2 3 4 5 6
-3-4-5 -2 -1 0 1 2 3-3-4 -2 -1 0 1 2 3 4-3-4 -2 -1 0 1 2 3 4
5-4
Example
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Chapter 5 25 Glencoe Algebra 1
Skills PracticeSolving Compound Inequalities
Graph the solution set of each compound inequality.
1. b > 3 or b ≤ 0 2. z ≤ 3 and z ≥ -2
3. k > 1 and k > 5 4. y < -1 or y ≥ 1
Write a compound inequality for each graph.
5. -2 -1-4 -3 0 1 2 3 4
6.
7. 8.
Solve each compound inequality. Then graph the solution set.
9. m + 3 ≥ 5 and m + 3 < 7 10. y - 5 < -4 or y - 5 ≥ 1
11. 4 < f + 6 and f + 6 < 5 12. w + 3 ≤ 0 or w + 7 ≥ 9
13. -6 < b - 4 < 2 14. p - 2 ≤ -2 or p - 2 > 1
Define a variable, write an inequality, and solve each problem. Check your solution.
15. A number plus one is greater than negative five and less than three.
16. A number decreased by two is at most four or at least nine.
17. The sum of a number and three is no more than eight or is more than twelve.
-3-4 -2 -1 0 1 2 3 4-2 -1 0 1 2 3 4 5 6
-3-4 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4
-2 -1 0 1 2 3 4 5 6-2 -1 0 1 2 3 4 5 6
-4 -3 -2 -1 0 1 2 3 4
-3-4 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4-3-4 -2 -1 0 1 2 3 4
-2 -1 0 1 2 3 4 5 6
-4 -3 -2 -1 0 1 2 3 4
5-4
0 1 2 3 4 5 6 7 8
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Chapter 5 26 Glencoe Algebra 1
PracticeSolving Compound Inequalities
Graph the solution set of each compound inequality.
1. -4 ≤ n ≤ 1 2. x > 0 or x < 3
3. g < -3 or g ≥ 4 4. -4 ≤ p ≤ 4
Write a compound inequality for each graph.
5. 6.
7. 8.
Solve each compound inequality. Then graph the solution set.
9. k - 3 < -7 or k + 5 ≥ 8 10. -n < 2 or 2n - 3 > 5
11. 5 < 3h + 2 ≤ 11 12. 2c - 4 > -6 and 3c + 1 < 13
Define a variable, write an inequality, and solve each problem. Check your solution.
13. Two times a number plus one is greater than five and less than seven.
14. A number minus one is at most nine, or two times the number is at least twenty-four.
15. METEOROLOGY Strong winds called the prevailing westerlies blow from west to east in a belt from 40° to 60° latitude in both the Northern and Southern Hemispheres.
a. Write an inequality to represent the latitude of the prevailing westerlies.
b. Write an inequality to represent the latitudes where the prevailing westerlies are not located.
16. NUTRITION A cookie contains 9 grams of fat. If you eat no fewer than 4 and no more than 7 cookies, how many grams of fat will you consume?
-3-4 -2 -1 0 1 2 3 4
-2 -1-4 -3-6 -5 0 1 2
-2 -1 0 1 2 3 4 5 6-2 -1-4 -3 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4-3-4 -2 -1 0 1 2 3 4
-2-3-4-5-6 -1 0 1 2-2 -1 0 1 2 3 4 5 6
-2 -1 0 1 2 3 4 5 6-4 -3 -2 -1 0 1 2 3 4
-2 -1-4 -3 0 1 2 3 4
0-1-2-3-4 1 2 3 4
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Chapter 5 27 Glencoe Algebra 1
Word Problem PracticeSolving Compound Inequalities
1. WEATHER Ken saw this graph in the newspaper weather forecast. It shows the predicted temperature range for the following day. Write an inequality to represent the number line graph.
2. POOLS The pH of a person’s eyes is 7.2. Therefore, the ideal pH for the water in a swimming pool is between 7.0 and 7.6. Write a compound inequality to represent pH levels that could cause physical discomfort to a person’s eyes.
3. STORE SIGNS In Randy’s town, street-side signs themselves must be exactly 8 feet high. When mounted on poles, the signs must be shorter than 20 feet or taller than 35 feet so that they do not interfere with the power and phone lines. Write a compound inequality to represent the possible height of the poles.
4. HEALTH The human heart circulates from 770,000 to 1,600,000 gallons of blood through a person’s body every year. How many gallons of blood does the heart circulate through the body in one day?
5. HEALTH Body mass index (BMI) is a measure of weight status. The BMI of a person over 20 years old is calculated using the following formula.
BMI = 703 × weight in pounds
−− (height in inches)2
The table below shows the meaning of different BMI measures.
Source: Centers for Disease Control
a. Write a compound inequality to represent the normal BMI range.
b. Write a compound inequality to represent an adult weight that is within the healthy BMI range for a person 6 feet tall.
62° 64° 66° 68° 70°60°58°56°54°52°50°F
5-4
BMI Weight Status
less than 18.5 underweight
18.5 – 24.9 normal
25 – 29.9 overweight
more than 30 obese
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Chapter 5 28 Glencoe Algebra 1
Enrichment
Some Properties of InequalitiesThe two expressions on either side of an inequality symbol are sometimes called the first and second members of the inequality.
If the inequality symbols of two inequalities point in the same direction, the inequalities have the same sense. For example, a < b and c < d have the same sense; a < b and c > d have opposite senses.
In the problems on this page, you will explore some properties of inequalities.
Three of the four statements below are true for all numbers a and b (or a, b, c, and d). Write each statement in algebraic form. If the statement is true for all numbers, prove it. If it is not true, give an example to show that it is false.
1. Given an inequality, a new and equivalent inequality can be created by interchanging the members and reversing the sense.
2. Given an inequality, a new and equivalent inequality can be created by changing the signs of both terms and reversing the sense.
3. Given two inequalities with the same sense, the sum of the corresponding members are members of an equivalent inequality with the same sense.
4. Given two inequalities with the same sense, the difference of the corresponding members are members of an equivalent inequality with the same sense.
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Chapter 5 29 Glencoe Algebra 1
Study Guide and Intervention Inequalities Involving Absolute Value
Inequalities Involving Absolute Value (<) When solving inequalities that involve absolute value, there are two cases to consider for inequalities involving < (or ≤).
Remember that inequalities with and are related to intersections.
Solve |3a + 4| < 10. Then graph the solution set.
Write � 3a + 4 � < 10 as 3a + 4 < 10 and 3a + 4 > -10. 3a + 4 < 10 and 3a + 4 > -10 3a + 4 - 4 < 10 - 4 3a + 4 - 4 > -10 - 4 3a < 6 3a > -14 3a −
3 < 6 −
3 3a −
3 > -14 −
3
a < 2 a > -4 2 − 3
The solution set is {a � -4 2 − 3 < a < 2} .
ExercisesSolve each inequality. Then graph the solution set.
1. � y � < 3 2. � x - 4 � < 4 3. � y + 3 � ≤ 2
-3-4 -2 -1 0 1 2 3 4 0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1 0
4. � b + 2 � ≤ 3 5. � w - 2 � ≤ 5 6. � t + 2 � ≤ 4
-6 -5 -4 -3 -2 -1 0 1 2 -8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8
7. � 2x � ≤ 8 8. � 5y - 2 � ≤ 7 9. � p - 0.2 � < 0.5
-3-4 -2 -1 0 1 2 3 4 -3-4 -2 -1 0 1 2 3 4 -0.8 -0.4 0 0.4 0.8
If � x � < n, then x > -n and x < n.
Now graph the solution set.
-2 -1-4-5 -3 0 1 2 3
5-5
Example
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Chapter 5 30 Glencoe Algebra 1
Study Guide and Intervention (continued)
Inequalities Involving Absolute Value
Solve Absolute Value Inequalities (>) When solving inequalities that involve absolute value, there are two cases to consider for inequalities involving > (or ≥). Remember that inequalities with or are related to unions.
Solve � 2b + 9 � > 5. Then graph the solution set.
Write � 2b + 9 � > 5 as � 2b + 9 � > 5 or � 2b + 9 � < -5.
2b + 9 > 5 or 2b + 9 < -5
2b + 9 - 9 > 5 - 9 2b + 9 - 9 < -5 - 9
2b > -4 2b < -14
2b − 2 > -4 −
2 2b −
2 < -14 −
2
b > -2 b < -7
The solution set is {b � b > -2 or b < -7} .
ExercisesSolve each inequality. Then graph the solution set.
1. � c - 2 � > 6 2. � x - 3 � > 0 3. � 3f + 10 � ≥ 4
20-2-4-6 4 6 8 10 0-1-2-3-4 1 2 3 4 -6 -5 -4 -3 -2 -1 0 1 2
4. � x � ≥ 2 5. � x � ≥ 3 6. � 2x + 1 � ≥ -2
-4 -3 -2 -1 0 1 2 3 4 0-1-2-3-4 1 2 3 4 0-1-2-3-4 1 2 3 4
7. � 2d - 1 � ≥ 4 8. � 3 - (x - 1) � ≥ 8 9. � 3r + 2 � > -5
-4 -3 -2 -1 0 1 2 3 4 -4 -2 0 2 4 6 8 10 12 0-1-2-3-4 1 2 3 4
5-5
-9 -8 -7 -6 -5 -4 -3 -2 0-1
Now graph the solution set.
Example
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Chapter 5 31 Glencoe Algebra 1
Skills PracticeInequalities Involving Absolute Value
Match each open sentence with the graph of its solution set.
1. � x � > 2 a. -2-3-4-5 -1 0 1 2 3 4 5
2. � x - 2 � ≤ 3 b. -2-3-4-5 -1 0 1 2 3 4 5
3. � x + 1 � < 4 c. -2-3-4 -1 0 1 2 3 4 5 6
Express each statement using an inequality involving absolute value.
4. The weatherman predicted that the temperature would be within 3° of 52°F.
5. Serena will make the B team if she scores within 8 points of the team average of 92.
6. The dance committee expects attendance to number within 25 of last year’s 87 students.
Solve each inequality. Then graph the solution set.
7. � x + 1 � < 0 8. � c - 3 � < 1
9. � n + 2 � ≥ 1 10. � t + 6 � > 4
11. � w - 2 � < 2 12. � k - 5 � ≤ 4
-8 -7-10 -9 -6 -5 -4 -3 -2 -1 0-2 -1-4-5-6 -3 0 1 2 3 4
-3 -1 0 1 2 3 4 5 6-2 7-3-4-5-6 -2 -1 0 1 2 3 4
5-5
-3-4 -2 -1 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 10
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Chapter 5 32 Glencoe Algebra 1
PracticeInequalities Involving Absolute Value
Match each open sentence with the graph of its solution set.
1. � x - 3 � ≥ 1 a.
2. � 2x + 1 � < 5 b.
3. � 5 - x � ≥ 3 c.
Express each statement using an inequality involving absolute value.
4. The height of the plant must be within 2 inches of the standard 13-inch show size.
5. The majority of grades in Sean’s English class are within 4 points of 85.
Solve each inequality. Then graph the solution set.
6. |2z - 9| ≤ 1 7. |3 - 2r| > 7
8. |3t + 6| < 9 9. |2g - 5| ≥ 9
Write an open sentence involving absolute value for each graph.
10. 11.
12. 13.
14. RESTAURANTS The menu at Jeanne’s favorite restaurant states that the roasted chicken with vegetables entree typically contains 480 Calories. Based on the size of the chicken, the actual number of Calories in the entree can vary by as many as 40 Calories from this amount.
a. Write an absolute value inequality to represent the situation.
b. What is the range of the number of Calories in the chicken entree?
-2-3 -1 0 1 2 3 4 5 6 7-2-3-4-5-6-7-8 -1 0 1 2
1 2 3 4 5 6 7 8 9 10 11
-2 -1 0 1 2 3 4 5 6 7 8-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5-5 -4 -3 -2 -1 0 1 2 3 4 5
-2-3-4-5 -1 0 1 2 3 4 5
-2 -1 0 1 2 3 4 5 6 7 8
-2-3-4-5 -1 0 1 2 3 4 5
5-5
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Chapter 5 33 Glencoe Algebra 1
Word Problem PracticeInequalities Involving Absolute Value
1. SPEEDOMETERS The government requires speedometers on cars sold in the United States to be accurate within ±2.5% of the actual speed of the car. If your speedometer reads 60 miles per hour while you are driving on a highway, what is the range of possible actual speeds at which your car could be traveling?
2. BAKING Pete is making muffins for a bake sale. Before he starts baking, he goes online to research different muffin recipes. The recipes that he finds all specify baking temperatures between 350°F and 400°F, inclusive. Write an absolute value inequality to represent the possible temperatures t called for in the muffin recipes Pete is researching.
3. ARCHERY In an Olympic archery event, the center of the target is set exactly 130 centimeters off the ground. To get the highest score of ten points, an archer must shoot an arrow no further than 3.05 centimeters from the exact center of the target.
a. Write an absolute value inequality to represent the possible distances dfrom the ground an archer can hit the target and still score ten points.
b. Graph the solution set of the inequality you wrote in part a.
124 126 128 130 132 134
4. CATS During a recent visit to the veterinarian’s office, Mrs. Van Allen was informed that a healthy weight for her cat is approximately 10 pounds, plus or minus one pound. Write an absolute value inequality that represents unhealthy weights w for her cat.
5. STATISTICS The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the individual scores deviate from the mean. For example, in a recent year the mean score on the mathematics section of the SAT test was 515 and the standard deviation was 114. This means that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean.
a. Write an absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean.
b. What is the range of SAT mathematics test scores ±2 standard deviation from the mean?
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Chapter 5 34 Glencoe Algebra 1
Enrichment
Precision of MeasurementThe precision of a measurement depends both on your accuracy in measuring and the number of divisions on the ruler you use. Suppose you measured a length of wood to the nearest one-eighth of an inch and got a length of 6 5 −
8 inches.
The drawing shows that the actual measurement lies somewhere
between 6 9 − 16
and 6 11 − 16
inches. This measurement can be written using
the symbol ±, which is read plus or minus. It can also be written as a compound inequality.
6 5 − 8 ± 1 −
16 in. 6 9 −
16 in. ≤ m ≤ 6 11 −
16 in.
In this example, 1 − 16
inch is the absolute error. The absolute error is
one-half the smallest unit used in a measurement.
Write each measurement as a compound inequality. Use the variable m.
1. 5 1 − 2 ± 1 −
4 in. 2. 3.78 ± 0.005 kg 3. 7.11 ± 0.005 g
4. 16 ± 1 − 2 yd 5. 22 ± 0.5 cm 6. 9 −
16 ± 1 −
32 in.
For each measurement, give the smallest unit used and the absolute error.
7. 9.5 in. ≤ m ≤ 10.5 in. 8. 4 1 − 4 in. ≤ m ≤ 4 3 −
4 in.
9. 23 1 −
2 cm ≤ m ≤ 24 1 −
2 cm 10. 7.135 mm ≤ m ≤ 7.145 mm
5 6 7 8
65–8
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Chapter 5 35 Glencoe Algebra 1
Graphing Calculator ActivityAbsolute Value Inequalities
The TEST menu can be used to solve and graph absolute value inequalities by using the equivalent compound inequalities related to absolute value.
ExercisesGraph and solve each inequality.
1. |x + 3| ≥ 2 2. |2x + 6| ≤ 4 3. ⎪ 2 - 4x −
5 ⎥ > 2 4. |x + 8| < -3
Graph and solve each inequality.
a. |x + 4| ≥ 8
Enter the inequality into Y1. Then enter the equivalent compound inequality into Y2 and graph to view the results. Be sure to choose appropriate settings for the view window.Keystrokes: MATH ENTER + 4 ) 2nd [TEST] 4 8
ENTER + 4 2nd [TEST] 6 (–) 8 2nd [TEST] 2
+ 4 2nd [TEST] 4 8 ENTER GRAPH .
Use TRACE to confirm the solution. When y = 1 the statement is true, and when y = 0 the statement is false. Thus, the solution is x ≤
-12 or x ≥ 4.
b. ⎪
5x + 2 −
4
⎥
≤ 7
Enter the inequality into Y1 and the equivalent compound inequalities into Y2. Then graph the solution set.Keystrokes: MATH ENTER ( 5 + 2 ) ÷ 4 )
2nd [TEST] 6 7 ENTER ( 5 + 2 ) ÷ 4 2nd
[TEST] 4 (–) 7 2nd [TEST] ENTER ( 5 + 2 )
÷ 4 2nd [TEST] 6 7 ENTER GRAPH .
The statement is true between -6 and 5.2. Thus the solution is -6 ≤ x ≤ 5.2.
[-18.8, 18.8] scl:2 by [-3.1, 3.1] scl:1
[-18.8, 18.8] scl:2 by [-3.1, 3.1] scl:1
[-18.8, 18.8] scl:2 by [-3.1, 3.1] scl:1
[-18.8, 18.8] scl:2 by [-3.1, 3.1] scl:1
5-5
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Chapter 5 36 Glencoe Algebra 1
Study Guide and InterventionGraphing Inequalities in Two Variables
Graph Linear Inequalities The solution set of an inequality that involves two variables is graphed by graphing a related linear equation that forms a boundary of a half-plane. The graph of the ordered pairs that make up the solution set of the inequality fill a region of the coordinate plane on one side of the half-plane.
Graph y ≤ -3x - 2.
Graph y = -3x - 2. Since y ≤ -3x - 2 is the same as y < -3x - 2 and y = -3x - 2, the boundary is included in the solution set and the graph should be drawn as a solid line.Select a point in each half plane and test it. Choose (0, 0) and (-2, -2). y ≤ -3x - 2 y ≤ -3x - 2 0 ≤ -3(0) - 2 -2 ≤ -3(-2) - 2 0 ≤ -2 is false. -2 ≤ 6 - 2
-2 ≤ 4 is true.The half-plane that contains (-2, -2) contains the solution. Shade that half-plane.
ExercisesGraph each inequality.
1. y < 4 2. x ≥ 1 3. 3x ≤ y
4. -x > y 5. x - y ≥ 1 6. 2x - 3y ≤ 6
7. y < - 1 − 2 x - 3 8. 4x - 3y < 6 9. 3x + 6y ≥ 12
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Chapter 5 37 Glencoe Algebra 1
Study Guide and Intervention (continued)
Graphing Inequalities in Two Variables
Solve Linear Inequalities We can use a coordinate plane to solve inequalities with one variable.
Use a graph to solve 2x + 2 > -1.
Step 1 First graph the boundary, which is the related function. Replace the inequality sign with an equals sign, and get 0 on a side by itself.
2x + 2 > -1 Original inequality
2x + 2 = -1 Change < to = .
2x + 2 + 1 = -1 + 1 Add 1 to each side.
2x + 3 = 0 Simplify.
Graph 2x + 3 = y as a dashed line.
Step 2 Choose (0, 0) as a test point, substituting these values into the original inequality give us 3 > -5.
Step 3 Because this statement is true, shade the half plane containing the point (0, 0).
Notice that the x-intercept of the graph is at -1 1 − 2 . Because the half-plane
to the right of the x-intercept is shaded, the solution is x > -1 1 − 2 .
ExercisesUse a graph to solve each inequality.
1. x + 7 ≤ 5 2. x - 2 > 2 3. -x + 1 < -3
4. -x - 7 ≥ -6 5. 3x - 20 < -17 6. -2x + 11 ≥ 15
5-6
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Chapter 5 38 Glencoe Algebra 1
Skills PracticeGraphing Inequalities in Two Variables
Match each inequality to the graph of its solution.
1. y - 2x < 2 a. b.
2. y ≤ -3x
3. 2y - x ≥ 4
4. x + y > 1
c. d.
Graph each inequality.
5. y < -1 6. y ≥ x - 5 7. y > 3x
8. y ≤ 2x + 4 9. y + x > 3 10. y - x ≥ 1
Use a graph to solve each inequality.
11. 1 > 2x + 5 12. 7 ≤ 3x + 4 13. - 1 − 2 < - 1 −
2 x + 1
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Chapter 5 39 Glencoe Algebra 1
PracticeGraphing Inequalities in Two Variables
Determine which ordered pairs are part of the solution set for each inequality.
1. 3x + y ≥ 6, {(4, 3), (-2, 4), (-5, -3), (3, -3)}
2. y ≥ x + 3, {(6, 3), (-3, 2), (3, -2), (4, 3)}
3. 3x - 2y < 5, {(4, -4), (3, 5), (5, 2), (-3, 4)}
Graph each inequality.
4. 2y - x < -4 5. 2x - 2y ≥ 8 6. 3y > 2x - 3
Use a graph to solve each inequality.
7. -5 ≤ x - 9 8. 6 > 2 − 3 x + 5 9. 1 −
2 > -2 x + 7 −
2
10. MOVING A moving van has an interior height of 7 feet (84 inches). You have boxes in 12 inch and 15 inch heights, and want to stack them as high as possible to fit. Write an inequality that represents this situation.
11. BUDGETING Satchi found a used bookstore that sells pre-owned DVDs and CDs. DVDs cost $9 each, and CDs cost $7 each. Satchi can spend no more than $35.
a. Write an inequality that represents this situation.
b. Does Satchi have enough money to buy 2 DVDs and 3 CDs?
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Chapter 5 40 Glencoe Algebra 1
1. FAMILY Tyrone said that the ages of his siblings are all part of the solution set of y > 2x, where x is the age of a sibling and y is Tyrone’s age. Which of the following ages is possible for Tyrone and a sibling?Tyrone is 23; Maxine is 14. Tyrone is 18; Camille is 8. Tyrone is 12; Francis is 4. Tyrone is 11; Martin is 6. Tyrone is 19; Paul is 9.
2. FARMING The average value of U.S. farm cropland has steadily increased in recent years. In 2000, the average value was $1490 per acre. Since then, the value has increased at least an average of $77 per acre per year. Write an inequality to show land values above the average for farmland.
3. SHIPPING An international shipping company has established size limits for packages with all their services. The total of the length of the longest side and the girth (distance completely around the package at its widest point perpendicular to the length) must be less than or equal to 419 centimeters. Write and graph an inequality that represents this situation.
4. FUNDRAISING Troop 200 sold cider and donuts to raise money for charity. They sold small boxes of donut holes for $1.25 and cider for $2.50 a gallon. In order to cover their expenses, they needed to raise at least $100. Write and graph an inequality that represents this situation.
5. INCOME In 2006 the median yearly family income was about $48,200 per year. Suppose the average annual rate of change since then is $1240 per year.
a. Write and graph an inequality for the annual family incomes y that are less than the median for x years after 2006.
b. Determine whether each of the following points is part of the solution set. (2, 51,000) (8, 69,200) (5, 50,000) (10, 61,000)
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Length
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150
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200
250
300
350
400
450
500g
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50 250 350200 300 400
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gal
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10
40
50
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70
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Years since 2006
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52,000
54,000
56,000
58,000y
321 5 7 8 9 104 6 x
length
girth
5-6 Word Problem PracticeGraphing Inequalities in Two Variables
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Chapter 5 41 Glencoe Algebra 1
Enrichment
Linear ProgrammingLinear programming can be used to maximize or minimize costs. It involves graphing a set of linear inequalities and using the region of intersection. You will use linear programming to solve the following problem.
Layne’s Gift Shoppe sells at most 500 items per week. To meet her customers’ demands, she sells at least 100 stuffed animals and 75 greeting cards. If the profit for each stuffed animal is $2.50 and the profit for each greeting card is $1.00, the equation P(a, g) = 2.50a + 1.00g can be used to represent the profit. How many of each should she sell to maximize her profit?
Write the inequalities: Graph the inequalities:a + g ≤ 500a ≥ 100g ≥ 75
Find the vertices of the triangle formed: (100, 75), (100, 400), and (425, 75) Substitute the values of the vertices into the equation found above: 2.50(100) + 1(75) = 325 2.50(100) + 1(400) = 650 2.50(425) + 1(75) = 1137.50 The maximum profit is $1137.50.
Exercises The Spirit Club is selling shirts and banners. They sell at most 400 of the two items. To meet the demands of the students, they must sell at least 50 T-shirts and 100 banners. The profit on each shirt is $4.00 and the profit on each banner is $1.50, the equation P(t, b) = 4.00t + 1.50b can be used to represent the profit. How many should they sell of each to maximize the profit?
1. Write the inequalities to represent this situation.
2. Graph the inequalities from Exercise 1.
3. Find the vertices of the figure formed.
4. What is the maximum profit the Spirit Club can make?
b
tO 100
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500
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200
200 300 400 500
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aO 100
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-500
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-200
200 300 400 500
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Chapter 5 42 Glencoe Algebra 1
Spreadsheet ActivityInequalities in Two Variables
You can use a spreadsheet to determine whether ordered pairs satisfy an inequality.
ExercisesUse a spreadsheet to determine which ordered pairs are part of the solution set for each inequality.
1. 2x + 3y > 1; {(0, 3), (1, -3), (-2, -1), (6, 8)}
2. 7x - y < 8; {(1, 2), (-3, -1), (0, -10), (6, 9)}
3. y ≥ 3x; {(3, 1), (-4, 5), (-1, 0), (7, -1), (2, 7)}
4. y ≤ -4x; {(9, 3), (-3, 5), (0, 0), (12, 1), (3, 9)}
5. y > 12 - 2x; {(-3, -3), (-1, 9), (12, 13), (-4, 11)}
6. y > 2 + 6x; {(0, -4), (-4, 8), (9, 17), (-2, 18), (-5, -5)}
7. |x + 1| ≤ y; {(1, -8), (0, 4), (5, 16), (-2, -8), (11, -2)}
8. |y - 7| < x; {(5, 8), (-1, 3), (2, 19), (-6, -6), (10, -22)}
Use a spreadsheet to determine which ordered pairs from the set {(2, 3), (4, 1), (-1, 2), (0, 7), (-8, -10)} are part of the solution set for 5x - 2y > 12.
Step 1 Use columns A and B of the spreadsheet for the replacement set. Enter the x-coordinates in column A and the y-coordinates in column B.
Step 2 Column C contains the formula for the inequality. Use the names of the cells containing the x- and y-coordinates of each ordered pair to determine whether that ordered pair is part of the solution set. The formula will return TRUE or FALSE.
The solution set contains the ordered pairs for which the inequality is true. The ordered pair {(4, 1)} is part of the solution set of 5x - 2y > 12.
The spreadsheet can also evaluate inequalities involving absolute value. Enter an absolute value expression like |x| using the function ABS(x).
A
1
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3
B Cy 5x - 2y > 12
=5*A2-2*B2>12
=5*A3-2*B3>12
=5*A4-2*B4>12
=5*A5-2*B5>12
=5*A6-2*B6>12
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Chapter 5 43 Glencoe Algebra 1
Student Recording Sheet
Use this recording sheet with pages 330 – 331 of the Student Edition.
5
Record your answers for Question 17 on the back of this paper.
Extended Response
10. 9.
10. (grid in)
11.
12.
13. (grid in)
14.
15.
16.
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Read each question. Then fill in the correct answer.
1. A B C D
2. F G H J
3. A B C D
4. F G H J
5. A B C D
6. F G H J
7. A B C D
8. F G H J
Multiple Choice
Record your answer in the blank.
For gridded response questions, also enter your answer in the grid by writing each number or symbol in a box. Then fill in the corresponding circle for that number or symbol.
Short Response/Gridded Response
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Chapter 5 44 Glencoe Algebra 1
Rubric for Scoring Extended Response
General Scoring Guidelines
• If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended response questions require the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete response for full credit.
Exercise 17 Rubric
5
Score Specifi c Criteria
4
The inequality written in part a shows that Theresa’s savings after w weeks is 35w and that she can take a vacation after saving at least $640 (35w ≥ 640). In part b, both sides of the inequality should be divided by 35 to get w ≥ 18 2 −
7 , and it should be noted that Theresa must save for 19 weeks (the
mixed number should be rounded up to the next largest integer). In part c, the inequality 45w ≥ 640 should be solved for w (w ≥ 14 2 −
9 ) . The student
should then show that the minimum time will be decreased by 19 – 5 or 4 weeks.
3 A generally correct solution, but may contain minor flaws in reasoning or computation.
2 A partially correct interpretation and/or solution to the problem.
1 A correct solution with no evidence or explanation.
0 An incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given.
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Chapter 5 45 Glencoe Algebra 1
For Questions 1 and 3, solve each inequality.
1. - d − 5 - 12 ≥ 8
2. 23 - t ≤ 2(t - 9) - 3(t + 2)
3. 16 < 3t - 2
4. Define a variable, write an inequality, and solve: The sum of a number and three is less than nineteen less the number.
5. MULTIPLE CHOICE Connor is mailing some letters at the post office. Stamps cost 44 cents each. He also needs to mail a package that costs $7.65. Which expression shows how many letters Connor can mail if he has $10.00 to spend in total?
A 7.65 + 0.44x > 10.00 C 7.65 + 0.44x ≥ 10.00 B 7.65 + 0.44x < 10.00 D 7.65 + 0.44x ≤ 10.00
1. Solve w + 9 ≤ -5. Then graph your solution on a number line.
2. Define a variable, write an inequality, and solve: A number decreased by 7 is at least 15.
Solve each inequality.
3. m − 13
> -6
4. -3n ≤ 84
5. MULTIPLE CHOICE Which inequality does not have the solution {x|x < -2}?
A -3x > 6 C 7x < -14
B - x − 2 < 1 D 4 −
3 x < -
8 − 3
Chapter 5 Quiz 1 (Lessons 5-1 and 5-2)
1.
2.
3.
4.
5.
Chapter 5 Quiz 2 (Lesson 5-3)
1.
-15-16-17-18 -14-13 -11-10-12
2.
3.
4.
5.
5
5
SCORE
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Chapter 5 46 Glencoe Algebra 1
Chapter 5 Quiz 3(Lessons 5-4 and 5-5)
1. Solve -1 < 2x - 1 ≤ 5. Then graph the solution set.
2. MULTIPLE CHOICE Which value of x is not a solution to 3x - 1 < 5 or 7 - x ≤ 3?
A 0 B 2 C 4 D 5
3. Solve ⎪ x - 1 −
2 ⎥ ≤ 1. Then graph the solution set.
4. Solve ⎪ 2x - 1 ⎪ ≥ 3. Then graph the solution set.
5. Write an open sentence involving absolute value for the graph shown.
1. MULTIPLE CHOICE Which is not true about the graph of 2x + y ≥ 1?
A The point (2, 2) is located inside the shaded region.
B The boundary is graphed as a solid line.
C The boundary is graphed along y = -2x + 1.
D The origin is located inside the shaded region.
2. Determine whether the test point (3, 3) is in the shaded half-plane of the graph of y + 2 ≤ 3x.
3. Use a graph to solve 1 − 3 x + 4 ≤ 3.
For Questions 4 and 5, graph each inequality.
4. x < 3
5. -2(x - y) ≤ 4
Chapter 5 Quiz 4 (Lesson 5-6)
1.
2.
3.
4.
5.
5
5
-4 -3 -2 -1 0 1 2 3 4
1.
2.
3.
4.
5.
-4 54321-3 0-1-2
-4 54321-3 0-1-2
-4 54321-3 0-1-2
y
xO
y
xO
y
xO
SCORE
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Chapter 5 47 Glencoe Algebra 1
SCORE
Part I Write the letter for the correct answer in the blank at the right of each question.
For Questions 1 – 5, solve each inequality.
1. r -
7−
8> 1
A {
r � �
r >
1 −
8 }
B {
r � �
r <
1 −
8 }
C {
r � �
r > 1
7 −
8 }
D {
r � �
r < 1
7 −
8 }
2. 12x + 5 ≥ 17x - 10
F {x � x ≤ -3} G {x � x ≥ 3} H {x � x ≥ -3} J {x � x ≤ 3}
3. 6m - 2(7 + 3m) > 5(2m - 3) - m
A {m � m < 1} B {
m � �
m < 1 −
9 }
C {m � m > 1} D {
m � �
m > 1 −
9 }
4. 2n −
7 ≤ 4
F {n � n ≤ 14} G {n � n ≥ 14} H {
n � �
n ≤ 8 −
7 }
J {
n � �
n ≥ 8 −
7 }
5. 3t - 2(t - 1) ≥ 5t - 4(2 + t) A
{
t � t ≤ -
5 −
7 }
C {t � all real numbers}
B {
t � t ≤ 3 −
4 }
D
Part II
6. Solve the inequality 4.2 > -11 + t. Check your solution.
7. Solve the inequality 2x – 1 > 7. Then graph the solution set.
Define a variable, write an inequality, and solve each problem.
8. For a package to qualify for a certain postage rate, the sum of its length and girth cannot exceed 85 inches. If the girth is 63 inches, how long can the package be?
9. The minimum daily requirement of vitamin C for 14-year-olds is at least 50 milligrams per day. An average-sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement?
1.
2.
3.
4.
5.
6.
7.
8.
9.
Chapter 5 Mid-Chapter Test (Lessons 5-1 through 5-3)
5
1 1098762 543
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Chapter 5 48 Glencoe Algebra 1
SCORE Chapter 5 Vocabulary Test
boundary
closed half-plane
compound inequality
half-plane
intersection
set-builder notation
system of inequalities
union
Choose a term from the vocabulary list above to complete the sentence.
1. An equation defines the or edge for each half-plane.
2. A containing and is true if both of the inequalities it contains are true.
3. The solution set for an inequality that contains twovariables consists of many ordered pairs which fill a region on the coordinate plane called a .
4. The graph of a compound inequality containing and is the of the graphs of the two inequalities.
5. The graph of a compound inequality containing or is the of the graphs of the two inequalities.
Define each term in your own words.
6. open half-plane
7. set-builder notation
1.
2.
3.
4.
5.
6.
7.
5
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Chapter 5 49 Glencoe Algebra 1
SCORE Chapter 5 Test, Form 1
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1–7, solve each inequality.
1. x - 7 > 3 A {x | x > 10} B {x | x > -4} C {x | x < 10} D {x | x < -4}
2. 3 ≥ t + 1 F {t ⎪ t ≤ 4} G {t | t ≥ 2} H {t ⎪ t ≤ 2} J {t ⎪ t ≥ 4}
3. 1 ≥ -y
− 4
A {y � � y ≥ -
1 − 4 } B {y | y ≥ -4} C {y | y ≤ 4} D {y | y ≤ 3}
4. 5m < -25 F {m | m < 125} G {m | m < -125} H {m | m > -5} J {m | m < -5}
5. -36 ≤ 3t A {t ⎪ t ≥ -12} B {t | t ≤ 12} C {t | t ≥ 12} D {t | t ≤ -12}
6. 6y - 8 > 4y + 26 F {y | y > -9} G {y ⎪ y > -17} H {y | y > 9} J {y ⎪ y > 17}
7. 3(2d - 1) ≥ 4(2d - 3) - 3 A {d | d ≥ -9} B {d ⎪ d ≤ -6} C {d | d ≥ 3} D {d ⎪ d ≤ 6}
8. Six is at least four more than a number. Which inequality represents this sentence?
F 6 ≤ n + 4 G 6 ≥ n + 4 H 4 ≤ n + 6 J 4 ≥ n + 6
9. More than eighteen students in an algebra class pass the first test. This is about three-fifths of the class. How many students are in the class?A less than 30 B less than 25 C more than 30 D 25
10. Phillip has between two hundred and three hundred baseball cards. Which inequality represents this situation?
F 200 < p < 300 H p < 300 or p < 200G 200 > p > 300 J p < 200 and p > 300
11. Which of the following is the graph of the solution set of m > -1 and m ≤ 1?
A C
B D
12. Which compound inequality has the solution set shown in the graph?
F x < -1 or x > 3 H x > -1 or x ≥ 3 G x > -1 or x < 3 J x ≤ -1 or x ≥ 3
-1-2-3-4 0 1 2 43
-1-2-3-4 0 1 2 43 -1-2-3-4 0 1 2 43
-1-2-3-4 0 1 2 43
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
-1-2-3-4 0 1 2 43
5
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Chapter 5 50 Glencoe Algebra 1
13. Which of the following is the solution set of 2a + 1 > 9 or a < -1?
A {a � a < -1 or a > 4} C {a � -1 ≤ a ≤ 4}
B {a � a ≤ -1 or a ≥ 4} D {a � a < -1 or a > 5}
14. Which inequality corresponds to the graph shown?
-2 -1-3 0 1 2 3 4 5
F �x - 3� ≤ 1 H �x - 3� ≥ 1 G �x - 1� ≤ 3 J �x - 1� ≥ 3
15. Solve � x - 3 � < 2. A {x � 1 < x < 5} C {x � -1 < x < 1} B {x � -5 < x < -1} D {x � -1 < x < 5}
16. Which inequality has the solution set shown in the graph?
F y < 1 H y > 1 G y ≤ 1 J y ≥ 1
17. Which inequality has the solution set shown in the graph?
A y < -x + 2 C y < -x + 1 B y > -x + 2 D y > -x + 1
18. Determine which of the ordered pairs are a part of the solution set for the inequality graphed at the right.
F (2, 1) H (-3, -3) G (1, 3) J (-2, -3)
19. Which inequality has a solution set of {x � x > 3 or x < -3}?
A � 2x � > 6 C � 2x � ≥ 6 B � 2x � < 6 D � 2x � ≤ 6
20. Juan’s income y consists of at least $37,500 salary plus 5% commission on all of his sales x. Which inequality represents Juan’s income in one year?
F y ≤ 37,500 + 5x H y ≥ 37,500 + 0.05x G y ≥ x + 0.05(37,500) J y ≥ 37,500 + 5
Bonus If x < 0, which integer does not satisfy the inequality x + 2 < 1?
13.
14.
15.
16.
17.
18.
19.
20.
Chapter 5 Test, Form 1 (continued)
y
x
y
xO
y
x
5
B:
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Chapter 5 51 Glencoe Algebra 1
SCORE
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1–6, solve each inequality.
1. -51 ≤ x + 38 A {x � x ≤ -13} B {x � x ≤ 89} C {x � x ≥ -89} D {x � x ≥ -13} 1.
2. m - 3 − 8 >
1 − 2
F = {m | | m > 7 −
8 } G {m |
| m < 7 − 8 } H {m |
| m < 1 − 8 } J {m |
| m > 1 − 8 } 2.
3. t − -2
> 4
A {t | t < -8} B {t | t < -2} C {t | t > 2} D {t | t > -8} 3.
4. -3.5z < 42 F {z | z > 12} G {z | z < 12} H {z | z < -12} J {z | z > -12} 4.
5. 4w - 6 > 6w - 20 A {w | w < 7} B {w | w < 2} C {w | w < -7} D {w | w < -2} 5.
6. 8r - (5r + 4) ≥ -31 F {r | r ≤ -9} G {r | r ≥ -9} H {r | r ≥ 9} J {r | r ≤ 9} 6.
7. The sum of two consecutive integers is at most 3. What is the greatest possible value for the greater integer?
A 5 B 1 C 3 D 2 7.
8. Which of the following is the graph of the solution set of y < -3 or y < 1?
F -1-2-3-4 0 1 2 43
H -1-2-3-4 0 1 2 43
G -1-2-3-4 0 1 2 43
J -1-2-3-4 0 1 2 43
8.
9. Which compound inequality has the solution set shown in the graph?
A -1 < n < 2 C n ≥ -1 or n < 2 B -1 ≤ n < 2 D -1 < n ≤ 2 9.
10. Which of the following is the solution set of -4 < 3t + 5 ≤ 20? F {t |-3 < t ≤ 5} H {t | t < -3} G {t | t < -3 and t ≤ 5} J {t | t < -3 or t ≥ 5} 10.
11. Which of the following is the graph of the solution set of t - 4 ≥ 4t + 8 or 3t > 14 - 4t?
A -1-2-3-4-5 0 1 2 3
C -1-2-3-4-5 0 1 2 3
B -1-2-3-4-5 0 1 2 3
D -1-2-3-4-5 0 1 2 3
11.
-1-2-3-4 0 1 2 43
Chapter 5 Test, Form 2A 5
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Chapter 5 52 Glencoe Algebra 1
12. Which inequality corrresponds to the graph shown?
-2 -1 0 1 2 3 4 5 6
F � x - 2 � < 3 H � x - 2 � ≥ 3 G � x - 2 � > 3 J � x - 2 � ≤ 3
13. Which of the following is the solution set of | 2x - 3 | > 4? A {x � x < -0.5 or x > 3.5} C {x � -0.5 < x < 3.5}
B {x � x < -1 or x > 7} D {x � x < 0.5 or x > 3.5}
14. Pete’s grade on a test was within 5 points of his class average of 94. What is his range of grades on the test?F g ≤ 89 or g ≥ 99 H g ≥ 89 or g ≥ 99
G 89 ≤ g ≤ 99 J g < 99 or g < 89
15. Which ordered pair is part of the solution set of the inequality 12 + y ≤ -3x? A (-16, 3) B (1, 4) C (4, -1) D (3, -16)
16. Which inequality is graphed at the right? F y < 2x + 1 H y < 1 −
2 x + 1
G y > 2x + 1 J y > 1 − 2 x + 1
17. Taka bought a new coat and new shoes. He spent $122. Which inequality represents this situation if x represents the cost of a coat and y represents the cost of the shoes he buys?
A 122 ≤ y + x B y ≤ 122 + x C y - x ≥ 122 D y ≤ 122 - x
18. Determine which of the ordered pairs are a part of the solution of y + 1 > 1 −
2 x + 3.
F (2, 3) G (-4, 0) H (1, 2) J (-3, 1)
19. Which inequality has a solution set of {x � x > -3 or x < -4}? A � 2x + 7 � < 1 C � 2x + 7 � > -1 B � 2x + 7 � > 1 D � 2x + 7 � > -1
20. Laurie and Maya sold at most $50 worth of get-well and friendship cards. The friendship cards, x, were sold for $2 each and the get-well cards, y, were sold for $1.50 each. Which point represents a reasonable number of cards sold?
F (20, 10) G (15, 10) H (18, 20) J (10, 30)
Bonus Solve 6(|n| - 3) - 4 |n| + 5 ≤ 11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Chapter 5 Test, Form 2A (continued)
y
xO
(0, 1) (2, 2)
5
B:
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Chapter 5 53 Glencoe Algebra 1
SCORE
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1 – 6, solve each inequality.
1. -13 > w + 12 A {w ⎪ w < -25} B {w ⎪ w > -25} C {w ⎪ w > -1} D {w ⎪ w < -1}
2. x - 1 −
4 ≤ -
1 −
2
F {
x �
�
x ≤ -
1 −
4 }
G {
x �
�
x ≤ -
3 −
4 }
H {
x �
�
x ≥ -
1
−
4
}
J {
x �
�
x ≥ -
3 −
4 }
3. m −
-5 < -3
A {m ⎪ m > -15} B {m ⎪ m < -15} C {m ⎪ m < 15} D {m ⎪ m > 15}
4. -1.1t ≤ 4.62 F {t ⎪ t ≤ 5.72} G {t ⎪ t ≥ 5.72} H {t ⎪ t ≤ -4.2} J {t ⎪ t ≥ -4.2}
5. 5z - 4 > 2z + 8 A {z ⎪ z > 4} B {z ⎪ z < 1} C {z ⎪ z < 4} D {z ⎪ z > 1}
6. 7 - 9r - (r + 12) ≤ 25 F {r ⎪ r ≤ -3} G {r ⎪ r ≤ -0.6} H {r ⎪ r ≥ -3} J {r ⎪ r ≥ -0.6}
7. The sum of two consecutive integers is at most 7. What is the largest possible value for the lesser integer?
A 1 B 3 C 2 D 5
8. Which of the following is the graph of the solution set of x > 0 or x < -4? F
-1-2-3-4-5-6 0 1 2 H
-1-2-3-4-5-6 0 1 2
G -1-2-3-4-5-6 0 1 2
J -1-2-3-4-5-6 0 1 2
9. Which compound inequality has the solution set shown in the graph?
A -2 < y < 3 C y ≥ -2 or y < 3 B -2 < y ≤ 3 D -2 ≤ y < 3
10. Which of the following is the solution set of -3 < 2x + 7 ≤ 13? F {x ⎪ -5 < x ≤ 3} H {x ⎪ x < -5} G {x ⎪ x < 3 or x > -5} J {x ⎪ -5 ≤ x < 3}
11. Which of the following is the graph of the solution set of 7a + 3 ≤ a - 15 or 5a - 3 < 8a?
A -1-2-3-4-5-6 0 1 2
C -1-2-3-4-5-6 0 1 2
B -1-2-3-4-5-6 0 1 2
D -1-2-3-4 0 1 2 43
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
-1-2-3-4 0 1 2 43
Chapter 5 Test, Form 2B5
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Chapter 5 54 Glencoe Algebra 1
12. Which inequality corresponds to the graph shown?
-4 -3 -2 -1 0 1 2 3 4
F � x - 3 � > 1 H � x - 1 � > 3
G � x - 3 � < 1 J � x - 1 � < 3
13. Which of the following is the solution set of 4 - 7x ≥ 3?
A {x | | x < 1 − 7 or x > 1} C {x | | x ≤ 1 −
7 or x ≥ 1}
B {x | x is a real number.} D {x | 1 ≤ x ≤ 7}
14. Katrina’s weight is within 8 pounds of her ideal weight of 120 pounds. What is her range of weight?F x ≥ 112 or x ≥ 128 H 112 ≥ x ≥ 128 G x ≤ 112 or x ≤ 128 J 112 ≤ x ≤ 128
15. Which ordered pair is part of the solution set of the inequality 5 - y ≤ -3x?
A (2, -1) B (-2, -1) C (-3, -5) D (3, -5)
16. Which inequality is graphed?
F y ≤ 2x - 1 H y ≤ -2x - 1 G y ≥ 2x - 1 J y ≥ -2x - 1
17. Alicia has at most $196 to buy a new baseball glove and a new baseball bat. Which inequality represents this situation?
A y ≤ 196 - x B y ≤ 196 + x C 196 ≤ y + x D y - x ≥ 196
18. Determine which of the ordered pairs are a part of the solution set of y + 3 < 2x - 1.F (0, 0) G (2, 0) H (0, -4) J (2, -2)
19. Which inequality has a solution set of {x � x > 4 and x < 8}?
A ⎪ 1 − 2 x - 3⎥ < 1 C ⎪ 1 −
2 x - 1⎥ < 3
B ⎪ 1 − 2 x - 3⎥ > 1 D ⎪ 1 −
2 x - 1⎥ > 3
20. Beng and Shim have less than $30 for candle-making supplies. The moldsx cost $6 each and the wax y is $2 per pound. Which point represents a reasonable number of molds and pounds of wax they could buy?
F (3, 4) G (4, 4) H (5, 1) J (3, 6)
Bonus Solve 2 - 3x < 5(2 - x) ≤ 3(2 - x) + 10.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Chapter 5 Test, Form 2B (continued)5
y
xO
B:
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Chapter 5 55 Glencoe Algebra 1
SCORE
1. Solve x - 12 > 1. Then graph your solution on a number line.
Solve each inequality.
2. 7 + z < 3
3. b − 8 > -
1 − 5
4. t − 6 ≥ 14
5. -19.8 ≥ 3.6y
6. -4r < 22
7. 4x - 5 < 2x + 11
8. 5(p + 2) - 2(p - 1) ≥ 7p + 4
9. 1.3(c - 4) ≤ 2.6 + 0.7c
Solve each compound inequality. Then graph the solution set.
10. 3w < 6 and -5 < w
11. -4 ≤ n or 3n + 1 < -2
12. -4x - 8 ≥ -4 or 7x - 5 < 16
For Questions 13 and 14, solve each inequality. Then graph the solution set.
13. � 1 - x � ≤ 2
14. � 3 - 2x � ≥ 1
Chapter 5 Test, Form 2C5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
-1-2-3-4 0 1 2 43
-1-2-3-4 0 1 2 43
-1-2-3-4 0 1 2 43
0-1-2-3-4 1 2 43
-1-2-3-4-5-6 0 1 2
131211109 14 15 1716
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Chapter 5 56 Glencoe Algebra 1
15. Solve �8x + 2� < 14.
16. Ian has $6000. He wants to buy a car within $1500 of this amount. Define a variable, write an open sentence, and find the range of car prices.
17. Graph y > - 1 − 3 x + 2.
18. Use a graph to solve 2x - 3y ≤ 6.
19. What inequality has the solution set shown in the graph?
20. EXPENSES Camille has no more than $20.00 to spend each week for lunch and bus fare. Lunch costs $3.00 each day, and bus fare is $0.75 each ride. Write an inequality for this situation. Can Camille buy lunch 5 times and ride the bus 8 times in one week?
Bonus Graph the solution set of the compound inequality 3 < � x - 4 � < 7.
Chapter 5 Test, Form 2C (continued)5
y
x
15.
16.
17.
18.
19.
20.
B:
y
xO
y
xO
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Chapter 5 57 Glencoe Algebra 1
SCORE
1. Solve y - 7 ≤ 5. Then graph your solution on a number line.
Solve each inequality.
2. 8 + k ≥ 13
3. h − 3 < 9
4. - 2 − 3 > z −
5
5. 9.8 ≥ 2.8k
6. -3m < -18
7. 5t + 8 ≤ 3t - 3
8. 3(-w - 6) < 2(2w + 8) + 1
9. 1.9 + 1.7x < 2.1(3 + x)
Solve each compound inequality. Then graph the solution set.
10. 7w > 14 and w < 3
11. w − 3 < 1 or 3w + 5 > 11
12. 2 + 3x > 8 or 4 - 7x ≤ -17
For Questions 13 and 14, solve each inequality. Then graph the solution set.
13. � z + 4 � ≥ 7
14. � w - 1 � ≤ 4
15. Solve � 2x - 5 � < 3.
Chapter 5 Test, Form 2D5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
-11 30
-1-2-3-4 0 1 2 43
0-1-2-3-4 1 2 3 4
-1-2-3-4 0 1 2 43
1312111098 14 15 16
-1-2-3 0 1 2 4 53
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Chapter 5 58 Glencoe Algebra 1
16. Abe has $4500. He wants to buy a boat within $1300 of this amount. Define a variable, write an open sentence, and find the range of boat prices.
17. Graph y ≤ 3x.
18. Use a graph to solve 2y - 4x < 8.
19. What inequality has the solution set shown in the graph?
20. SHOPPING Matthew is shopping for shoes and socks. He has $75.00 to spend. The shoes he likes cost $28.00, and the socks cost $4.00. Write an inequality for this situation. Can Matthew buy 2 pairs of shoes and 5 pairs of socks?
Bonus Graph the solution set of the compound inequality | x + 1 | < 4 or | x + 1 | ≥ 6.
y
x
Chapter 5 Test, Form 2D (continued)5
16.
17.
18.
19.
20.
B:
y
xO
y
xO
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Chapter 5 59 Glencoe Algebra 1
SCORE
Solve each inequality. Then graph your solution on a number line.
1. m - (-3.4) ≥ 12.7
2. t + (-4) < 32
Define a variable, write an inequality, and solve each problem.
3. Negative three sevenths plus a number is at least 2.
4. A number less 15 is greater than the sum of twice the number and 8.
Solve each inequality.
5. -2.6 ≥ w − 4
6. -11t < -9
7. 2 - 3b > 11 - 15b − 7
8. 5x - 3(x - 6) ≤ 0
9. -3x + 2(6x - 7) > 4(3 - 2x) + 17x - 8
Define a variable, write an inequality, and solve each problem.
10. Raul plans to spend no more than $78.00 on two shirts and a pair of jeans. He bought the two shirts for $19.89 each. How much can he spend on the jeans?
11. The sum of two consecutive positive even integers is at most 15. What are the possible pairs of integers?
12. Susan makes 10% commission on her sales. She also receives a salary of $25,600. How much must she sell to receive a total income between $32,500 and $41,900?
Chapter 5 Test, Form 35
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
3635343332 37 38 4039
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Chapter 5 60 Glencoe Algebra 1
Solve each compound inequality, and graph the solution set.
13. - n − 2 < 3 or 2n - 3 > 12
14. 2(x - 14) - x < 7(x + 2) + x ≤ x + 70
For Questions 15–17, solve each inequality. Then graph the solution set.
15. |-4x + 8 | < 16
16. | 5x - 3 | ≥ 17
17. ⎪ 3 - 2x −
5 ⎥ ≥ 1
18. Graph -y ≤ 3x.
19. Use a graph to solve x + 3y > -12.
20. DOGS Each afternoon Maria walks the dogs at a local pet shelter for up to 2 hours. Maria spends 16 minutes walking a large dog and 12 minutes walking a small dog. Write an inequality for this situation. If Maria walked 9 dogs in one afternoon, what is the greatest number of large dogs that she could have walked that afternoon?
Bonus If xy < 0, determine if the compound inequality, 2x + 1 > 7 and 4 - y < 3, is true or false. Explain your reasoning.
Chapter 5 Test, Form 3 (continued)5
13.
14.
-6 80
15.
16.
17.
18.
19.
20.
B:
-1-2-3-4-5-6-7-8-9
-1-2 0 1 2 4 5 63
-1-2 0 1 2 4 5 63
y
xO
y
xO
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Chapter 5 61 Glencoe Algebra 1
SCORE Chapter 5 Extended-Response Test
Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.
1. Solve 10n - 7(n + 2) > 5n - 12. Explain each step in your solution.
2. Draw a line on a coordinate plane so that you can determine at least two points on the graph.
a. Write an inequality to represent one of the half planes created by the line.
b. Determine if the solution set of the inequality written for part a includes the line or not. Explain your response.
3. Let b > 2. Describe how you would determine if ab > 2a.
4. Determine if the open sentence | x - 2 | > 4 and the compound inequality -2x < 4 or x > 6 have the same solution set.
5. ARCHITECTURE An architect is designing a house for the Frazier family. In the design, she must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built is 158 feet long, and 90 feet wide.
a. The building codes state that one can build no closer than 20 feet to the lot line. Write an inequality to represent the possible widths of the house along the 90-foot dimension. Solve the inequality.
b. The Fraziers requested that the rectangular house contain no less than 2800 square feet and no more than 3200 square feet of floor space. If the house has only one floor, use the maximum value for the width of the house from part a, and explain how to use an inequality to find the possible lengths.
c. The Fraziers have asked that the cost of the house be about $175,000 and are willing to deviate from this price no more than $20,000. Write an open sentence involving an absolute value and solve. Explain the meaning of the answer.
5
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Chapter 5 62 Glencoe Algebra 1
SCORE
1. Which equation is not equivalent to x - 7 = 12? (Lesson 2-2)
A x - 9 = 14 B x - 10 = 9 C x = 19 D x - 3 = 16
2. Find the value of y so that the line through (2, 3) and (5, y) has a slope of -2. (Lesson 3-3)
F -3 G 3 − 2 H 9 J 9 −
2
3. Solve -8x - 15 = -31. (Lesson 2-3)
A 22 B 6 C 2 D 26
4. If f (x) = 3(x - 5), find f (4). (Lesson 1-7)
F 7 G 27 H -3 J 3
5. Which equation shows the slope-intercept form of the line passing through (0, 1) and (2, 0)? (Lesson 4-2)
A y = -2x + 1 B y = 1 − 2 x -1 C y = 2x - 1 D y = - 1 −
2 x + 1
6. Write a compound inequality for the graph shown below. (Lesson 5-4)
F -1 < x ≤ 2 H -1 ≤ x < 2 G x ≤ -1 or x > 2 J x < -1 or x ≥ 2
7. Solve - 1 − 3 h ≤ 6. (Lesson 5-2)
A h ≤ –2 B h ≤ -18 C h ≥ -2 D h ≥ -18
8. Solve h + 3 ≥ 2. (Lesson 5-1)
F h ≤ 2 G h ≥ -1 H h ≥ 5 J h ≤ -1
9. Solve 4x + 12 > 2. (Lesson 5-3)
A x > -2 1 − 2 B x > -40 C x > 2 1 −
2 D x > 3 1 −
2
10. Which of the following is an arithmetic sequence? (Lesson 3-5)
F 1, 3, 6, 10, … H 34, 35, 38, 43, … G 5, 8, 11, 14, … J 1, 4, 9, 16, …
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. F G H J
F G H J
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
5 Standardized Test Practice(Chapters 1–5)
-3 -2 -1 0 1 2 3 4 5
A B C D
A B C D
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Chapter 5 63 Glencoe Algebra 1
11. Determine which is a linear equation. (Lesson 3-1)
A 1 − x – y = 7 C 3 = xy
B x2 – 4 = y D x - y = 4
12. Find the discounted price. Pants: $24 (Lesson 2-7)
Discount: 15%F $20.40 G $3.60 H $20 J $9
13. Solve 8x - 5 = 23 + 4x. (Lesson 2-4)
A 4.5 B 7 C 23 D 5
14. Rewrite 5(a - b + c) using the Distributive Property. (Lesson 1-4)
F 5a - b + c H 5a - 5b + 5cG 5a + 5b + c J 5a + b + c
15. Write an equation that passes through (3, 2) and has a slope of -2. (Lesson 4-3)
A y = 8x - 2 C y = -2x + 7 B y = -2x + 8 D y = -2x + 2
16. Find the slope of the line that passes through (-7, 8) and (-6, 5). (Lesson 3-3)
F -3 G - 1 − 3 H 3 J -6
17. Evaluate the expression if x = 4, y = 3, and z = 2. (Lesson 1-2)
x2 + 4y + z A 27 B 22 C 20 D 30
11.
12.
13.
14.
15.
16.
17. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
18. What is the slope of a line parallel to the line that passes through (-3, 1) and (3, 7)? (Lesson 4-4)
19. If m + 3 ≥ 14, then complete the inequality m - 6 ≥ . (Lesson 5-1)
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
0
?
5 Standardized Test Practice (continued)
Part 2: Gridded Response
Instructions: Enter your answer by writing each digit of the answer in a column box
and then shading in the appropriate circle that corresponds to that entry.
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Chapter 5 64 Glencoe Algebra 1
20. Solve a −
6 - 5 = 12. (Lesson 2-3)
21. If f (x) = x2 - 4x, find f (-3). (Lesson 1-7)
22. Solve y = 1 − 4 x - 1 if the domain is {-4, -2, 0, 2, 4}. (Lesson 1-5)
23. Write the slope-intercept form of an equation of the line that passes through (0, -4) and is parallel to the graph of 4x - y = 7. (Lesson 4-4)
24. Solve 4 − 5 a ≤ -12. (Lesson 5-2)
25. Solve the proportion 0.6 − x = 0.3 − 5 . (Lesson 2-6)
26. Graph 2x + 3y ≥ -9. (Lesson 5-6)
27. Solve ⎪3f + 2⎥ ≤ 7. Then graph the solution set. (Lesson 5-5)
28. Solve -5 ≤ 2a- 1 < 9. Then graph the solution set. (Lesson 5-4)
29. Graph the equation y = x - 4. (Lesson 3-1)
30. Mark is shopping during a computer store’s 20% sale. He is considering buying computers that range in cost from $500 to $1000.
a. How much are the computers after the 20% discount? (Lesson 5-4)
b. If sales tax is 7%, how much should Mark expect to pay? (Lesson 5-4)
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30a.
30b.
y
xO
5 Standardized Test Practice (continued)
Part 3: Short Response
Instructions: Write your answers in the space provided.
-4 -3 -2 -1 0 1 2 3 4
-3 -2 -1 0 1 2 3 4 5
y
xO
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Chapter 5 A1 Glencoe Algebra 1
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
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DAT
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Cha
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er y
ou a
gree
or
disa
gree
, wri
te N
S (
Not
Su
re).
ST
EP
1A
, D, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
Acc
ordi
ng
to t
he
Add
itio
n P
rope
rty
of I
neq
ual
itie
s, a
ddin
g an
y n
um
ber
to e
ach
sid
e of
a t
rue
ineq
ual
ity
wil
l re
sult
in
a
tru
e in
equ
alit
y.
2.
Th
e in
equ
alit
y m
+ 2
3 ≥
35
can
be
solv
ed b
y ad
din
g 23
to
each
sid
e.
3.
16 i
s n
o gr
eate
r th
an t
he
dif
fere
nce
of
a n
um
ber
and
12
can
be
wri
tten
as
16 ≤
n –
12.
4.
If b
oth
sid
es o
f r −
12
< 4
are
mu
ltip
lied
by
12, t
he
resu
lt i
s r
< 4
8.
5.
Th
e re
sult
of
divi
din
g bo
th s
ides
of
the
ineq
ual
ity
–2y
≥ 1
0 by
–2
is y
≥ –
5.
6.
To
solv
e an
in
equ
alit
y in
volv
ing
mu
ltip
lica
tion
, su
ch a
s 9t
> 2
7, d
ivis
ion
is
use
d.
7.
To
solv
e th
e in
equ
alit
y 8x
– 2
< 7
0, f
irst
div
ide
by 8
an
d th
en a
dd 2
.
8.
A c
ompo
un
d in
equ
alit
y is
an
in
equ
alit
y co
nta
inin
g m
ore
than
on
e va
riab
le.
9.
On
a n
um
ber
lin
e, a
clo
sed
dot
is u
sed
for
an i
neq
ual
ity
con
tain
ing
the
sym
bol
≥ o
r ≤
.10
. If
⎪t⎥
< 8
, th
en t
equ
als
all
nu
mbe
rs b
etw
een
0 a
nd
8.11
. O
n t
he
grap
h o
f y
> 2
x – 3
, th
e so
luti
on s
et w
ill
be a
ll
nu
mbe
rs a
bove
th
e gr
aph
of
the
lin
e y
= 2
x – 3
.
Aft
er y
ou c
omp
lete
Ch
ap
ter
5
•
Rer
ead
each
sta
tem
ent
and
com
plet
e th
e la
st c
olu
mn
by
ente
rin
g an
A o
r a
D.
•
Did
an
y of
you
r op
inio
ns
abou
t th
e st
atem
ents
ch
ange
fro
m t
he
firs
t co
lum
n?
•
For
th
ose
stat
emen
ts t
hat
you
mar
k w
ith
a D
, use
a p
iece
of
pape
r to
wri
te a
n
exam
ple
of w
hy
you
dis
agre
e.
Step
1
5 Step
2
A A A AD A AD D D D
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10
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PM
Answers (Anticipation Guide and Lesson 5-1)
Lesson 5-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
5 G
lenc
oe A
lgeb
ra 1
Stud
y G
uide
and
Inte
rven
tion
So
lvin
g I
neq
ualiti
es b
y A
dd
itio
n a
nd
Su
btr
acti
on
Solv
e In
equ
alit
ies
by
Ad
dit
ion
Add
itio
n c
an b
e u
sed
to s
olve
in
equ
alit
ies.
If
any
nu
mbe
r is
add
ed t
o ea
ch s
ide
of a
tru
e in
equ
alit
y, t
he
resu
ltin
g in
equ
alit
y is
als
o tr
ue.
Ad
dit
ion
Pro
per
ty o
f In
equ
alit
ies
Fo
r a
ll nu
mb
ers
a,
b,
an
d c
, if a
> b
, th
en
a +
c >
b +
c,
an
d if
a <
b,
the
n a
+ c
< b
+ c
.
Th
e pr
oper
ty i
s al
so t
rue
wh
en >
an
d <
are
rep
lace
d w
ith
≥ a
nd
≤.
S
olve
x -
8 ≤
-6.
T
hen
gra
ph
th
e so
luti
on.
x
- 8
≤ -
6 O
rigin
al in
equalit
y
x
- 8
+ 8
≤ -
6 +
8
Add 8
to e
ach s
ide.
x
≤ 2
S
implif
y.
Th
e so
luti
on i
n s
et-b
uil
der
not
atio
n i
s {x
|x ≤
2}.
Nu
mbe
r li
ne
grap
h:
-4
-3
-2
-1
01
23
4
S
olve
4 -
2a
> -
a. T
hen
gr
aph
th
e so
luti
on.
4
- 2
a >
-a
Ori
gin
al in
equalit
y
4
- 2
a +
2a
> -
a +
2a
Add 2
a to
each s
ide.
4
> a
S
implif
y.
a
< 4
4 >
a is t
he s
am
e a
s a
< 4
.
The
sol
utio
n in
set
-bui
lder
not
atio
n is
{a|
a <
4}.
Nu
mbe
r li
ne
grap
h:
-2
-1
01
23
45
6
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
Ch
eck
you
r so
luti
on, a
nd
th
en g
rap
h i
t on
a n
um
ber
lin
e.
1. t
- 1
2 ≥
16
{t �
t ≥
28}
2. n
- 1
2 <
6 {
n �
n <
18}
3.
6 ≤
g -
3 {
g �
g ≥
9}
2627
2829
3031
3233
34
14
1512
1316
1718
1920
78
910
1112
1314
15
4. n
- 8
< -
13 {
n �
n <
-5}
5.
-12
> -
12 +
y {
y �
y <
0}
6. -
6 >
m -
8 {
m �
m <
2}
-9
-10
-8
-7
-6
-5
-4
-3
-2
-3
-4
-2
-1
01
23
4
-
4-
2-
10
12
3-
34
Sol
ve e
ach
in
equ
alit
y. C
hec
k y
our
solu
tion
.
7. -
3x ≤
8 -
4x
8. 0
.6n
≥ 1
2 -
0.4
n
9. -
8k -
12
< -
9k
{
x �
x ≤
8}
{n
� n
≥ 1
2}
{k
� k
< 1
2}
10. -
y -
10
> 1
5 -
2y
11. z
- 1 −
3 ≤
4 −
3
12. -
2b >
-4
- 3
b
{
y �
y >
25}
{
z �
z ≤
1 2 −
3 }
{b
� b
> -
4}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k
you
r so
luti
on.
13–1
5. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
13. A
nu
mbe
r de
crea
sed
by 4
is
less
th
an 1
4. n
- 4
< 1
4; {
n �
n <
18}
14. T
he
diff
eren
ce o
f tw
o n
um
bers
is
mor
e th
an 1
2, a
nd
one
of t
he
nu
mbe
rs i
s 3.
n
- 3
> 1
2; {
n �
n >
15}
or
3 -
n >
12;
{n
� n
< -
9}
15. F
orty
is
no
grea
ter
than
th
e di
ffer
ence
of
a n
um
ber
and
2. 4
0 ≤
n -
2;
{n �
n ≥
42}
5-1
Exam
ple
1Ex
amp
le 2
001_
012_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
512
/21/
10
4:37
PM
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A1A01_A12_ALG1_A_CRM_C05_AN_661384.indd A1 12/21/10 6:14 PM12/21/10 6:14 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 5 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
6 G
lenc
oe A
lgeb
ra 1
Stud
y G
uide
and
Inte
rven
tion
(c
onti
nu
ed)
So
lvin
g I
neq
ualiti
es b
y A
dd
itio
n a
nd
Su
btr
acti
on
Solv
e In
equ
alit
ies
by
Sub
trac
tio
n S
ubtr
acti
on c
an b
e us
ed t
o so
lve
ineq
ualit
ies.
If
any
num
ber
is s
ubtr
acte
d fr
om e
ach
side
of
a tr
ue i
nequ
alit
y, t
he r
esul
ting
ine
qual
ity
is a
lso
true
.
Su
btr
acti
on
Pro
per
ty o
f In
equ
alit
ies
Fo
r a
ll nu
mb
ers
a,
b,
an
d c
, if a
> b
, th
en
a -
c >
b -
c,
an
d if
a <
b,
the
n a
- c
< b
- c
.
Th
e pr
oper
ty i
s al
so t
rue
wh
en >
an
d <
are
rep
lace
d w
ith
≥ a
nd
≤.
S
olve
3a
+ 5
> 4
+ 2
a. T
hen
gra
ph
it
on a
nu
mb
er l
ine.
3a
+ 5
> 4
+ 2
a O
rigin
al in
equalit
y
3a +
5 -
2a
> 4
+ 2
a -
2a
Subtr
act
2a
from
each s
ide.
a
+ 5
> 4
S
implif
y.
a
+ 5
- 5
> 4
- 5
S
ubtr
act
5 f
rom
each s
ide.
a
> -
1 S
implif
y.
Th
e so
luti
on i
s {a
�a >
-1}
.N
um
ber
lin
e gr
aph
: -
4-
3-
2-
10
12
34
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
Ch
eck
you
r so
luti
on, a
nd
th
en g
rap
h i
t on
a n
um
ber
lin
e.
1. t
+ 1
2 ≥
8
2. n
+ 1
2 >
-12
3.
16
≤ h
+ 9
{
t � t
≥ -
4}
{n
� n
> -
24}
{h
� h
≥ 7
}
-6
-5
-4
-3
-2
-1
01
2
-
26-
25-
24-
23-
22-
21
5
67
89
1011
1213
4. y
+ 4
> -
2
5. 3
r +
6 >
4r
6. 3 −
2 q
- 5
≥ 1 −
2 q
{
y �
y >
-6}
{
r � r
< 6
} {
q �
q ≥
5}
-8
-7
-6
-5
-4
-3
-2
-1
0
2
34
56
79
18
21
03
45
67
8
Sol
ve e
ach
in
equ
alit
y. C
hec
k y
our
solu
tion
. 7
. 4p
≥ 3
p +
0.7
8.
r +
1 −
4 >
3 −
8
9. 9
k +
12
> 8
k
{
p �
p ≥
0.7
} {
r � r
> 1 −
8 }
{k
� k
> -
12}
10. -
1.2
> 2
.4 +
y
11. 4
y <
5y+
14
12. 3
n +
17
< 4
n
{
y �
y <
-3.
6}
{y
� y
> -
14}
{n
� n
> 1
7}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k y
our
solu
tion
. 13
–15.
Sam
ple
an
swer
: L
et n
= t
he
nu
mb
er.
13. T
he
sum
of
a n
um
ber
and
8 is
les
s th
an 1
2. n
+ 8
< 1
2; {
n �
n <
4}
14. T
he
sum
of
two
nu
mbe
rs i
s at
mos
t 6,
an
d on
e of
th
e n
um
bers
is
-2.
n
+ (
-2)
≤ 6
; {n
� n
≤ 8
}
15. T
he s
um o
f a
num
ber
and
6 is
gre
ater
tha
n or
equ
al t
o -
4. n
+ 6
≥ -
4; {
n �
n ≥
-10
}
5-1
Exam
ple
001_
012_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
612
/21/
10
4:37
PM
Lesson 5-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
7 G
lenc
oe A
lgeb
ra 1
Skill
s Pr
acti
ceS
olv
ing
In
eq
ualiti
es b
y A
dd
itio
n a
nd
Su
btr
acti
on
Mat
ch e
ach
in
equ
alit
y to
th
e gr
aph
of
its
solu
tion
.
1. x
+ 1
1 >
16
c a.
-
8-
7-
6-
5-
4-
3-
2-
10
2. x
- 6
< 1
e
b.
3. x
+ 2
≤ -
3 a
c.
4. x
+ 3
≥ 1
b
d.
5. x
- 1
< -
7 d
e.
Sol
ve e
ach
in
equ
alit
y. C
hec
k y
our
solu
tion
, an
d t
hen
gra
ph
it
on a
nu
mb
er l
ine.
6. d
- 5
≤ 1
{d
� d
≤ 6
} 7.
t +
9 <
8 {
t � t
< -
1}
2
30
14
56
78
-2
-1
-4
-3
01
23
4
8. a
- 7
> -
13 {
a �
a >
-6}
9.
w -
1 <
4 {
w �
w <
5}
-8
-7
-6
-5
-4
-3
-2
-1
0
2
30
14
56
78
10. 4
≥ k
+ 3
{k
� k
≤ 1
} 11
. -9
≤ b
- 4
{b
� b
≥ -
5}
-
2-
1-
4-
30
12
34
-8
-7
-6
-5
-4
-3
-2
-1
0
12. -
2 ≥
x +
4 {
x �
x ≤
-6}
13
. 2y
< y
+ 2
{y
� y
< 2
}
-
6-
5-
8-
7-
4-
3-
2-
10
-2
-1
-4
-3
01
23
4
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m.
Ch
eck
you
r so
luti
on.
14–1
8. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
14. A
nu
mbe
r de
crea
sed
by 1
0 is
gre
ater
th
an -
5. n
- 1
0 >
-5;
{n
� n
> 5
}
15. A
nu
mbe
r in
crea
sed
by 1
is
less
th
an 9
. n
+ 1
< 9
; {n
� n
< 8
}
16. S
even
mor
e th
an a
num
ber
is l
ess
than
or
equa
l to
-18
. n
+ 7
≤ -
18; {
n �
n ≤
-25
}
17. T
wen
ty l
ess
than
a n
um
ber
is a
t le
ast
15.
n -
20
≥ 1
5; {
n �
n ≥
35}
18. A
nu
mbe
r pl
us
2 is
at
mos
t 1.
n +
2 ≤
1;
{n �
n ≤
-1}
-8
-7
-6
-5
-4
-3
-2
-1
087
65
43
21
0
43
21
0-
1-
2-
3-
4
5-1
87
65
43
21
0
001_
012_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
712
/21/
10
4:37
PM
Answers (Lesson 5-1)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A2A01_A12_ALG1_A_CRM_C05_AN_661384.indd A2 12/21/10 6:14 PM12/21/10 6:14 PM
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 5 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
8 G
lenc
oe A
lgeb
ra 1
5-1
Mat
ch e
ach
in
equ
alit
y w
ith
its
cor
resp
ond
ing
grap
h.
1. -
8 ≥
x -
15
b
a.
-6
-5
-4
-3
-2
-1
01
2
2. 4
x +
3 <
5x
d
b.
87
65
43
21
0
3. 8
x >
7x
- 4
a
c.
-8
-7
-6
-5
-4
-3
-2
-1
0
4. 1
2 +
x ≤
9 c
d
. 2
34
56
78
10
Sol
ve e
ach
in
equ
alit
y. C
hec
k y
our
solu
tion
, an
d t
hen
gra
ph
it
on a
nu
mb
er l
ine.
5. r
- (
-5)
> -
2 {r
| r >
- 7
} 6.
3x
+ 8
≥ 4
x {x
| x ≤
8}
-8
-7
-6
-5
-4
-3
-2
-1
0
4
52
36
78
910
7. n
- 2
.5 ≥
-5
{n | n
≥ -
2.5
} 8.
1.5
< y
+ 1
{y | y
> 0
.5}
-4
-3
-2
-1
01
23
4
-
4-
3-
2-
10
12
34
9. z
+ 3
> 2
−
3 10
. 1 −
2 ≤
c -
3 −
4
-4
-3
-2
-1
01
23
4
-
4-
3-
2-
10
12
34
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k
you
r so
luti
on.
11. T
he
sum
of
a n
um
ber
and
17 i
s n
o le
ss t
han
26.
n
+ 1
7 ≥
26;
{n
| n ≥
9}
12. T
wic
e a
nu
mbe
r m
inu
s 4
is l
ess
than
th
ree
tim
es t
he
nu
mbe
r. 2n
- 4
< 3
n;
{n | n
> -
4}
13. T
wel
ve i
s at
mos
t a
nu
mbe
r de
crea
sed
by 7
. 12
≤ n
- 7
; {n
| n ≥
19}
14. E
igh
t pl
us
fou
r ti
mes
a n
um
ber
is g
reat
er t
han
fiv
e ti
mes
th
e n
um
ber.
8 +
4n
> 5
n;
{n | n
< 8
}
15. A
TMO
SPH
ERIC
SC
IEN
CE
Th
e tr
opos
pher
e ex
ten
ds f
rom
th
e E
arth
’s s
urf
ace
to a
hei
ght
of 6
–12
mil
es, d
epen
din
g on
th
e lo
cati
on a
nd
the
seas
on. I
f a
plan
e is
fly
ing
at a
n
alti
tude
of
5.8
mil
es, a
nd
the
trop
osph
ere
is 8
.6 m
iles
dee
p in
th
at a
rea,
how
mu
ch
hig
her
can
th
e pl
ane
go w
ith
out
leav
ing
the
trop
osph
ere?
16. E
AR
TH S
CIE
NC
E M
atu
re s
oil
is c
ompo
sed
of t
hre
e la
yers
, th
e u
pper
mos
t be
ing
tops
oil.
Jam
al i
s pl
anti
ng
a bu
sh t
hat
nee
ds a
hol
e 18
cen
tim
eter
s de
ep f
or t
he
root
s. T
he
inst
ruct
ion
s su
gges
t an
add
itio
nal
8 c
enti
met
ers
dept
h f
or a
cu
shio
n. I
f Ja
mal
wan
ts t
o ad
d ev
en m
ore
cush
ion
, an
d th
e to
psoi
l in
his
yar
d is
30
cen
tim
eter
s de
ep, h
ow m
uch
m
ore
cush
ion
can
he
add
and
stil
l re
mai
n i
n t
he
tops
oil
laye
r?
Prac
tice
So
lvin
g I
neq
ualiti
es b
y A
dd
itio
n a
nd
Su
btr
acti
on
11-
14. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
no
mo
re t
han
2.8
mi
no
mo
re t
han
4 c
m
{z | z
> -
2 1 −
3 }
{c | c
≥ 1
1 −
4 }
001_
012_
ALG
1_A
_CR
M_C
05_C
R_6
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4.in
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10
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PM
Lesson 5-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
9 G
lenc
oe A
lgeb
ra 1
Wor
d Pr
oble
m P
ract
ice
So
lvin
g I
neq
ualiti
es b
y A
dd
itio
n a
nd
Su
btr
acti
on
1.SO
UN
D T
he
lou
dest
in
sect
on
Ear
th i
s th
e A
fric
an c
icad
a. I
t pr
odu
ces
sou
nds
as
lou
d as
105
dec
ibel
s at
20
inch
es a
way
. T
he
blu
e w
hal
e is
th
e lo
ude
st m
amm
al
on E
arth
. Th
e ca
ll o
f th
e bl
ue
wh
ale
can
re
ach
lev
els
up
to 8
3 de
cibe
ls l
oude
r th
an
the
Afr
ican
cic
ada.
How
lou
d ar
e th
e ca
lls
of t
he
blu
e w
hal
e?
2. G
AR
BA
GE
Th
e am
oun
t of
gar
bage
th
at
the
aver
age
Am
eric
an a
dds
to a
lan
dfil
l da
ily
is 4
.6 p
oun
ds. I
f at
lea
st 2
.5 p
oun
ds
of a
per
son
’s d
aily
gar
bage
cou
ld b
e re
cycl
ed, h
ow m
uch
wil
l st
ill
go i
nto
a
lan
dfil
l?
3. S
HO
PPIN
G T
yler
has
$75
to
spen
d at
th
e m
all.
He
purc
has
es a
mu
sic
vide
o fo
r $1
4.99
an
d a
pair
of
jean
s fo
r $1
8.99
. He
also
spe
nt
$4.7
5 fo
r lu
nch
. Tyl
er s
till
w
ants
to
purc
has
e a
vide
o ga
me.
How
m
uch
mon
ey c
an h
e sp
end
on a
vid
eo
gam
e?
4. S
UPR
EME
CO
UR
T T
he
firs
t C
hie
f Ju
stic
e of
th
e U
.S. S
upr
eme
Cou
rt, J
ohn
Ja
y, s
erve
d 20
79 d
ays
as C
hie
f Ju
stic
e.
He
serv
ed 1
0,46
3 da
ys f
ewer
th
an J
ohn
M
arsh
all,
wh
o se
rved
as
Su
prem
e C
ourt
C
hie
f Ju
stic
e fo
r th
e lo
nge
st p
erio
d of
ti
me.
How
man
y da
ys m
ust
th
e cu
rren
t S
upr
eme
Cou
rt C
hie
f Ju
stic
e Jo
hn
R
ober
ts s
erve
to
surp
ass
Joh
n M
arsh
all’s
re
cord
of
serv
ice?
5. W
EATH
ER T
heo
dore
Fu
jita
of
the
Un
iver
sity
of
Ch
icag
o de
velo
ped
a cl
assi
fica
tion
of
torn
adoe
s ac
cord
ing
to
win
d sp
eed
and
dam
age.
Th
e ta
ble
show
s th
e cl
assi
fica
tion
sys
tem
.
Lev
elN
ame
Win
d S
pee
d R
ang
e (m
ph
)
F0
Ga
le4
0 –
72
F1
Mo
de
rate
73
–11
2
F2
Sig
nifi
ca
nt
113
–15
7
F3
Seve
re15
8–
20
6
F4
Deva
sta
tin
g2
07
–2
60
F5
Incre
dib
le2
61
–3
18
F6
Inco
nce
iva
ble
319
–3
79
Sou
rce:
Nat
iona
l Wea
ther
Ser
vice
a. S
upp
ose
an F
3 to
rnad
o h
as w
inds
th
at
are
162
mil
es p
er h
our.
Wri
te a
nd
solv
e an
in
equ
alit
y to
det
erm
ine
how
m
uch
th
e w
inds
wou
ld h
ave
to
incr
ease
bef
ore
the
F3
torn
ado
beco
mes
an
F4
torn
ado.
16
2 +
x ≥
207
; x
≥ 4
5; a
t le
ast
45 m
ph
b.
A t
orn
ado
has
win
d sp
eeds
th
at a
re a
t le
ast
158
mil
es p
er h
our.
Wri
te a
nd
solv
e an
in
equ
alit
y th
at d
escr
ibes
how
m
uch
gre
ater
th
ese
win
d sp
eeds
are
th
an t
he
slow
est
torn
ado.
40 +
y ≥
158
; y ≥
118
; at
leas
t 11
8 m
ph
less
th
an 1
88 d
ecib
els
no
mo
re t
han
2.1
po
un
ds
per
day
.
Tyle
r ca
n s
pen
d n
o m
ore
than
$36
.27
on
a v
ideo
gam
e.
x >
12,
542;
mo
re t
han
12,
542
day
s
5-1
001_
012_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
912
/21/
10
4:37
PM
Answers (Lesson 5-1)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A3A01_A12_ALG1_A_CRM_C05_AN_661384.indd A3 12/21/10 6:14 PM12/21/10 6:14 PM
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ht © G
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cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
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Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
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PDF Pass
Chapter 5 A4 Glencoe Algebra 1
Lesson 5-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
11
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
So
lvin
g I
neq
ualiti
es b
y M
ult
iplicati
on
an
d D
ivis
ion
Solv
e In
equ
alit
ies
by
Mu
ltip
licat
ion
If
each
sid
e of
an
in
equ
alit
y is
mu
ltip
lied
by
the
sam
e po
siti
ve n
um
ber,
the
resu
ltin
g in
equ
alit
y is
als
o tr
ue.
How
ever
, if
each
sid
e of
an
in
equ
alit
y is
mu
ltip
lied
by
the
sam
e n
egat
ive
nu
mbe
r, th
e di
rect
ion
of
the
ineq
ual
ity
mu
st
be r
ever
sed
for
the
resu
ltin
g in
equ
alit
y to
be
tru
e.
Mu
ltip
licat
ion
Pro
per
ty o
f In
equ
alit
ies
Fo
r a
ll nu
mb
ers
a,
b,
an
d c
, w
ith
c ≠
0,
1.
if c
is p
ositiv
e a
nd
a >
b,
the
n a
c >
bc;
if c
is p
ositiv
e a
nd
a <
b,
the
n a
c <
bc;
2.
if c
is n
ega
tive
an
d a
> b
, th
en
ac
< b
c;if c
is n
ega
tive
an
d a
< b
, th
en
ac
> b
c.
Th
e pr
oper
ty i
s al
so t
rue
wh
en >
an
d <
are
rep
lace
d w
ith
≥ a
nd
≤.
S
olve
- y −
8 ≤
12.
- y −
8 ≥
12
Orig
inal in
equalit
y
(-8)
(- y −
8 ) ≤
(-
8)12
M
ultip
ly e
ach s
ide b
y -
8; change ≥
to ≤
.
y
≤ -
96
Sim
plif
y.
Th
e so
luti
on i
s { y
� y ≤
-96
}.
S
olve
3 −
4 k
< 1
5.
3 −
4 k
< 1
5 O
rigin
al in
equalit
y
( 4 −
3 ) 3
−
4 k <
( 4 −
3 ) 1
5 M
ultip
ly e
ach s
ide b
y 4
− 3
.
k
< 2
0 S
implif
y.
Th
e so
luti
on i
s {k
� k
< 2
0}.
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
Ch
eck
you
r so
luti
on.
1. y −
6 ≤
2
2. -
n
−
50 >
22
3. 3 −
5 h
≥ -
3 4.
- p −
6 <
-6
{
y �
y ≤
12}
{
n �
n <
-11
00}
{
h �
h ≥
-5}
{
p �
p >
36}
5.
1 −
4 n
≥ 1
0 6.
- 2 −
3 b
< 1 −
3
7. 3m
−
5
< -
3 −
20
8.
-2.
51 ≤
- 2h
−
4
{
n �
n ≥
40}
{b
� b
> -
1 −
2 }
{m
� m
< -
1 −
4 }
{h
� h
≤ 5
.02}
9. g −
5 ≥
-2
10. -
3 −
4 >
- 9p
−
5
11.
n
−
10 ≥
5.4
12
. 2a
−
7
≥ -
6
{
g �
g ≥
-10
} {p
� p
>
5 −
12
} {
n �
n ≥
54}
{
a �
a ≥
-21
}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k
you
r so
luti
on.
13–1
5. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
13. H
alf
of a
nu
mbe
r is
at
leas
t 14
. 1 −
2 n
≥ 1
4; {
n �
n ≥
28}
14. T
he
oppo
site
of
one-
thir
d a
nu
mbe
r is
gre
ater
th
an 9
. -
1 −
3 n
> 9
; {n
� n
< -
27}
15. O
ne
fift
h o
f a
nu
mbe
r is
at
mos
t 30
. 1 −
5 n
≤ 3
0; {
n �
n ≤
150
}
5-2
Exam
ple
1Ex
amp
le 2
001_
012_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
1112
/21/
10
4:37
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
10
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Tria
ng
le I
neq
ualiti
es
Rec
all
that
a l
ine
segm
ent
can
be
nam
ed b
y th
e le
tter
s of
its
en
dpoi
nts
. Lin
e se
gmen
t A
B (
wri
tten
as
−−
AB
) h
as p
oin
ts A
an
d B
for
en
dpoi
nts
. Th
e le
ngt
h o
f A
B i
s w
ritt
en w
ith
out
the
bar
as A
B.
AB
> B
C
m
∠ A
< m
∠ B
Th
e st
atem
ent
on t
he
left
abo
ve s
how
s th
at −
−
AB
is
shor
ter
than
−−−
BC
. T
he
stat
emen
t on
th
e ri
ght
abov
e sh
ows
that
th
e m
easu
re o
f an
gle
A
is l
ess
than
th
at o
f an
gle
B.
Th
ese
thre
e in
equ
alit
ies
are
tru
e fo
r an
y tr
ian
gle
AB
C,
no
mat
ter
how
lon
g th
e si
des.
a. A
B +
BC
> A
Cb
. If
AB
> A
C, t
hen
m∠
C >
m∠
B.
c. I
f m
∠C
> m
∠B
, th
en A
B >
AC
.
B
AC
Use
th
e th
ree
tria
ngl
e in
equ
alit
ies
for
thes
e p
rob
lem
s.
1. L
ist
the
side
s of
tri
angl
e D
EF
in
ord
er o
f in
crea
sin
g le
ngt
h.
D
FE
60°
35°
85°
−−
DF , −
−
DE
, −−
EF
2. I
n t
he
figu
re a
t th
e ri
ght,
wh
ich
lin
e se
gmen
t is
th
e sh
orte
st?
JM
K
L
65°
60°
65°
55°
65°
50°
−
−
LM
3. E
xpla
in w
hy
the
len
gth
s 5
cen
tim
eter
s, 1
0 ce
nti
met
ers,
an
d 20
cen
tim
eter
s co
uld
not
be
use
d to
mak
e a
tria
ngl
e. 5
+ 1
0 is
no
t g
reat
er t
han
20.
4. T
wo
side
s of
a t
rian
gle
mea
sure
3 i
nch
es a
nd
7 in
ches
. Bet
wee
n w
hic
h t
wo
valu
es m
ust
th
e th
ird
side
be?
4 in
. an
d 1
0 in
.
5. I
n t
rian
gle
XY
Z, X
Y =
15,
YZ
= 1
2, a
nd
XZ
= 9
. Wh
ich
an
gle
has
th
e gr
eate
st m
easu
re?
Wh
ich
has
th
e le
ast?
∠ Z
; ∠
Y
6. L
ist
the
angl
es ∠
A, ∠
C, ∠
AB
C, a
nd
∠A
BD
, in
ord
er o
f in
crea
sin
g si
ze.
C ADB
13 1512
5 9
∠
AB
D, ∠
A, ∠
AB
C, ∠
C
5-1
001_
012_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
1012
/21/
10
4:37
PM
Answers (Lesson 5-1 and Lesson 5-2)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A4A01_A12_ALG1_A_CRM_C05_AN_661384.indd A4 12/21/10 6:15 PM12/21/10 6:15 PM
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 5 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
12
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(c
onti
nu
ed)
So
lvin
g I
neq
ualiti
es b
y M
ult
iplicati
on
an
d D
ivis
ion
Solv
e In
equ
alit
ies
by
Div
isio
n I
f ea
ch s
ide
of a
tru
e in
equ
alit
y is
div
ided
by
the
sam
e po
siti
ve n
um
ber,
the
resu
ltin
g in
equ
alit
y is
als
o tr
ue.
How
ever
, if
each
sid
e of
an
in
equ
alit
y is
div
ided
by
the
sam
e n
egat
ive
nu
mbe
r, th
e di
rect
ion
of
the
ineq
ual
ity
sym
bol
mu
st b
e re
vers
ed f
or t
he
resu
ltin
g in
equ
alit
y to
be
tru
e.
Div
isio
n P
rop
erty
o
f In
equ
alit
ies
Fo
r a
ll nu
mb
ers
a,
b,
an
d c
with
c ≠
0,
1.
if c
is p
ositiv
e a
nd
a >
b,
the
n a −
c >
b
−
c ; if c
is p
ositiv
e a
nd
a <
b,
the
n a −
c <
b
−
c ;
2. if c
is n
ega
tive
an
d a
> b
, th
en
a −
c <
b
−
c ; if c
is n
ega
tive
an
d a
< b
, th
en
a −
c >
b
−
c .
Th
e pr
oper
ty i
s al
so t
rue
wh
en >
an
d <
are
rep
lace
d w
ith
≥ a
nd
≤.
S
olve
-12
y ≥
48.
-12
y ≥
48
Ori
gin
al in
equalit
y
-12
y −
-
12
≤
48
−
-12
D
ivid
e e
ach s
ide b
y -
12 a
nd c
hange ≥
to ≤
.
y
≤ -
4 S
implif
y.
Th
e so
luti
on i
s {y
� y
≤ -
4}.
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
Ch
eck
you
r so
luti
on.
1. 2
5g ≥
-10
0 2.
-2x
≥ 9
3.
-5c
> 2
4.
-8m
< -
64
{
g �
g ≥
-4}
{
x �
x ≤
-4
1 −
2 }
{c �
c <
- 2 −
5 }
{m
� m
> 8
}
5. -
6k <
1 −
5
6. 1
8 <
-3b
7.
30
< -
3n
8. -
0.24
< 0
.6w
{
k �
k >
- 1 −
30
} {
b �
b <
-6}
{
n �
n <
-10
} {
w �
w >
-0.
4}
9. 2
5 ≥
-2m
10
. -30
> -
5p
11. -
2n ≥
6.2
12
. 35
< 0
.05h
{m
� m
≥ -
12 1 −
2 }
{p
� p
> 6
} {
n �
n ≤
-3.
1}
{h
� h
> 7
00}
13. -
40 >
10h
14
. - 2 −
3n
≥ 6
15
. -3
< p −
4
16
. 4
> -
x −
2
{
h �
h <
-4}
{
n �
n ≤
-9}
{
p �
p >
-12
} {
x �
x >
-8}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. T
hen
ch
eck
yo
ur
solu
tion
.
17. F
our
tim
es a
nu
mbe
r is
no
mor
e th
an 1
08.
4n ≤
108
; {n
� n
≤ 2
7}
18. T
he
oppo
site
of
thre
e ti
mes
a n
um
ber
is g
reat
er t
han
12.
-3n
> 1
2; {
n �
n <
-4}
19. N
egat
ive
five
tim
es a
nu
mbe
r is
at
mos
t 10
0. -
5n ≤
10
0; {
n �
n ≥
-20
}
5-2
Exam
ple
17–1
9. S
amp
le a
nsw
er:
Let
n =
the
nu
mb
er.
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Lesson 5-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
13
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceS
olv
ing
In
eq
ualiti
es b
y M
ult
iplicati
on
an
d D
ivis
ion
Mat
ch e
ach
in
equ
alit
y w
ith
its
cor
resp
ond
ing
stat
emen
t.
1. 3
n <
9 d
a.
Th
ree
tim
es a
nu
mbe
r is
at
mos
t n
ine.
2. 1 −
3 n
≥ 9
f
b. O
ne
thir
d of
a n
um
ber
is n
o m
ore
than
nin
e.
3. 3
n ≤
9 a
c.
Neg
ativ
e th
ree
tim
es a
nu
mbe
r is
mor
e th
an n
ine.
4. -
3n >
9 c
d
. Th
ree
tim
es a
nu
mbe
r is
les
s th
an n
ine.
5. 1 −
3 n
≤ 9
b
e. N
egat
ive
thre
e ti
mes
a n
um
ber
is a
t le
ast
nin
e.
6. -
3n ≥
9 e
f.
On
e th
ird
of a
nu
mbe
r is
gre
ater
th
an o
r eq
ual
to
nin
e.
Sol
ve e
ach
in
equ
alit
y. C
hec
k y
our
solu
tion
.
7. 1
4g >
56
8. 1
1w ≤
77
9. 2
0b ≥
-12
0 10
. -8r
< 1
6
{
g �
g >
4}
{w
� w
≤ 7
} {
b �
b ≥
-6}
{
r � r
> -
2}
11. -
15p
≤ -
90
12.
x −
4 <
9
13.
a −
9 ≥
-15
14
. - p −
7 >
-9
{
p �
p ≥
6}
{x
� x
< 3
6}
{a
� a
≥ -
135}
{
p �
p <
63}
15. -
t
−
12 ≥
6
16. 5
z <
-90
17
. -13
m >
-26
18
. k −
5 ≤
-17
{
t � t
≤ -
72}
{z
� z
< -
18}
{m
� m
< 2
} {
k �
k ≤
-85
}
19. -
y <
36
20. -
16c
≥ -
224
21. -
h
−
10 ≤
2
22. 1
2 >
d
−
12
{
y �
y >
-36
} {
c �
c ≤
14}
{
h �
h ≥
-20
} {
d �
d <
144
}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m.
Ch
eck
you
r so
luti
on.
23–2
7. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
23. F
our
tim
es a
nu
mbe
r is
gre
ater
th
an -
48.
4n >
-48
; {n
� n
> -
12}
24. O
ne
eigh
th o
f a
nu
mbe
r is
les
s th
an o
r eq
ual
to
3. 1
−
8 n ≤
3;
{n �
n ≤
24}
25. N
egat
ive
twel
ve t
imes
a n
um
ber
is n
o m
ore
than
84.
-12
n ≤
84;
{n
� n
≥ -
7}
26. N
egat
ive
one
sixt
h o
f a
nu
mbe
r is
les
s th
an -
9. -
1 −
6 n
< -
9; {
n �
n >
54}
27. E
igh
t ti
mes
a n
um
ber
is a
t le
ast
16.
8n ≥
16;
{n
� n
≥ 2
}
5-2
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Answers (Lesson 5-2)
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-Hill C
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PDF Pass
Chapter 5 A6 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
14
Gle
ncoe
Alg
ebra
1
Mat
ch e
ach
in
equ
alit
y w
ith
its
cor
resp
ond
ing
stat
emen
t.
1. -
4n ≥
5 d
a.
Neg
ativ
e fo
ur
tim
es a
nu
mbe
r is
les
s th
an f
ive.
2. 4 −
5 n
> 5
f
b. F
our
fift
hs
of a
nu
mbe
r is
no
mor
e th
an f
ive.
3. 4
n ≤
5 e
c.
Fou
r ti
mes
a n
um
ber
is f
ewer
th
an f
ive.
4. 4 −
5 n
≤ 5
b
d. N
egat
ive
fou
r ti
mes
a n
um
ber
is n
o le
ss t
han
fiv
e.
5. 4
n <
5 c
e.
Fou
r ti
mes
a n
um
ber
is a
t m
ost
five
.
6. -
4n <
5 a
f.
Fou
r fi
fth
s of
a n
um
ber
is m
ore
than
fiv
e.
Sol
ve e
ach
in
equ
alit
y. C
hec
k y
our
solu
tion
.
7. -
a −
5
< -
14
8. -
13h
≤ 5
2 9.
b −
16
≥ -
6 10
. 39
> 1
3p
{
a �
a >
70}
{
h �
h ≥
-4}
{
b �
b ≥
-96
} {
p �
p <
3}
11.
2 −
3 n
> -
12
12. -
5 −
9 t
< 2
5 13
. - 3 −
5 m
≤ -
6 14
. 10
−
3 k
≥ -
10
{
n �
n >
-18
} {
t � t
> -
45}
{m
� m
≥ 1
0}
{k
� k
≥ -
3}
15. -
3b ≤
0.7
5 16
. -0.
9c >
-9
17. 0
.1x
≥ -
4 18
. -2.
3 <
j −
4
{
b �
b ≥
-0.
25}
{c
� c
< 1
0}
{x
� x
≥ -
40}
{j
� j >
-9.
2}
19. -
15y
< 3
20
. 2.6
v ≥
-20
.8
21. 0
> -
0.5u
22
. 7 −
8 f
≤ -
1
{
y �
y >
- 1 −
5 }
{v
� v
≥ -
8}
{u
� u
> 0
} {
f � f
≤ -
8 −
7 }
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k
you
r so
luti
on.
23–2
5. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
23. N
egat
ive
thre
e ti
mes
a n
um
ber
is a
t le
ast
57.
-3n
≥ 5
7; {
n �
n ≤
-19
}
24. T
wo
thir
ds o
f a
nu
mbe
r is
no
mor
e th
an -
10.
2 −
3 n
≤ -
10;
{n �
n ≤
-15
}
25. N
egat
ive
thre
e fi
fth
s of
a n
um
ber
is l
ess
than
-6.
- 3 −
5 n
< -
6; {
n �
n >
10}
26. F
LOO
DIN
G A
riv
er i
s ri
sin
g at
a r
ate
of 3
in
ches
per
hou
r. If
th
e ri
ver
rise
s m
ore
than
2
feet
, it
wil
l ex
ceed
flo
od s
tage
. How
lon
g ca
n t
he
rive
r ri
se a
t th
is r
ate
wit
hou
t ex
ceed
ing
floo
d st
age?
27. S
ALE
S P
et S
upp
lies
mak
es a
pro
fit
of $
5.50
per
bag
on
its
lin
e of
nat
ura
l do
g fo
od. I
f th
e st
ore
wan
ts t
o m
ake
a pr
ofit
of
no
less
th
an $
5225
on
nat
ura
l do
g fo
od, h
ow m
any
bags
of
dog
foo
d do
es i
t n
eed
to s
ell?
5-2
Prac
tice
So
lvin
g I
neq
ualiti
es b
y M
ult
iplicati
on
an
d D
ivis
ion
no
mo
re t
han
8 h
at le
ast
950
bag
s
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 5-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
15
Gle
ncoe
Alg
ebra
1
1.PI
ZZA
Tar
a an
d fr
ien
ds o
rder
a p
izza
. T
ara
eats
3 o
f th
e 10
sli
ces
and
pays
$4
.20
for
her
sh
are.
Ass
um
ing
that
Tar
a h
as p
aid
at l
east
her
fai
r sh
are,
wri
te a
n
ineq
alit
y fo
r h
ow m
uch
th
e pi
zza
cou
ld
hav
e co
st.
2.A
IRLI
NES
On
ave
rage
, at
leas
t 25
,000
pi
eces
of
lugg
age
are
lost
or
mis
dire
cted
ea
ch d
ay b
y U
nit
ed S
tate
s ai
rlin
es. O
f th
ese,
98%
are
loc
ated
by
the
airl
ines
w
ith
in 5
day
s. F
rom
a g
iven
day
’s l
ost
lugg
age,
at
leas
t h
ow m
any
piec
es o
f lu
ggag
e ar
e st
ill
lost
aft
er 5
day
s?
3.SC
HO
OL
Gil
ear
ned
th
ese
scor
es o
n t
he
firs
t th
ree
test
s in
bio
logy
th
is t
erm
: 86,
88
, an
d 78
. Wh
at i
s th
e lo
wes
t sc
ore
that
G
il c
an e
arn
on
th
e fo
urt
h a
nd
fin
al t
est
of t
he
term
if
he
wan
ts t
o h
ave
an
aver
age
of a
t le
ast
83?
4.EV
ENT
PLA
NN
ING
Th
e D
own
tow
n
Com
mu
nit
y C
ente
r do
es n
ot c
har
ge a
re
nta
l fe
e as
lon
g as
a r
ente
e or
ders
a
min
imu
m o
f $5
000
wor
th o
f fo
od f
rom
th
e ce
nte
r. A
nto
nio
is
plan
nin
g a
ban
quet
fo
r th
e Q
uar
terb
ack
Clu
b. I
f h
e is
ex
pect
ing
225
peop
le t
o at
ten
d, w
hat
is
the
min
imu
m h
e w
ill
hav
e to
spe
nd
on
food
per
per
son
to
avoi
d pa
yin
g a
ren
tal
fee?
$2
2.23
5. P
HY
SIC
S T
he
den
sity
of
a su
bsta
nce
de
term
ines
wh
eth
er i
t w
ill
floa
t or
si
nk
in a
liq
uid
. Th
e de
nsi
ty o
f w
ater
is
1 gr
am p
er m
illi
lite
r. A
ny
obje
ct w
ith
a
grea
ter
den
sity
wil
l si
nk
and
any
obje
ct
wit
h a
les
ser
den
sity
wil
l fl
oat.
Den
sity
is
giv
en b
y th
e fo
rmu
la d
= m
−
v
, wh
ere
m i
s m
ass
and
v is
vol
um
e. H
ere
is a
ta
ble
of c
omm
on c
hem
ical
sol
uti
ons
and
thei
r de
nsi
ties
.
So
luti
on
Den
sity
(g
/mL
)
concentr
ate
d c
alc
ium
chlo
ride
1.40
70
% iso
pro
pyl a
lco
ho
l0
.92
Sour
ce:
Amer
ican
Che
mis
try
Cou
ncil
a. P
last
ics
vary
in
den
sity
wh
en t
hey
are
m
anu
fact
ure
d; t
her
efor
e, t
hei
r vo
lum
es a
re v
aria
ble
for
a gi
ven
mas
s.
A t
able
t of
pol
ysty
ren
e (a
m
anu
fact
ure
d pl
asti
c) s
inks
in
wat
er
and
in a
lcoh
ol s
olu
tion
an
d fl
oats
in
ca
lciu
m c
hlo
ride
sol
uti
on. T
he
tabl
et
has
a m
ass
of 0
.4 g
ram
. Wh
at i
s th
e m
ost
its
volu
me
can
be?
b.
Wh
at i
s th
e le
ast
its
volu
me
can
be?
Wor
d Pr
oble
m P
ract
ice
So
lvin
g I
neq
ualiti
es b
y M
ult
iplicati
on
an
d D
ivis
ion
5-2 at le
ast
500
pie
ces
80
x ≤
$14
0.43
5 g
0.28
6 g
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Answers (Lesson 5-2)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A6A01_A12_ALG1_A_CRM_C05_AN_661384.indd A6 12/21/10 6:15 PM12/21/10 6:15 PM
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pyr
ight
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Chapter 5 A7 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
16
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Qu
ad
rati
c I
neq
ualiti
es
Lik
e li
nea
r in
equ
alit
ies,
in
equ
alit
ies
wit
h h
igh
er d
egre
es c
an a
lso
be s
olve
d. Q
uad
rati
c in
equ
alit
ies
hav
e a
degr
ee o
f 2.
Th
e fo
llow
ing
exam
ple
show
s h
ow t
o so
lve
quad
rati
c in
equ
alit
ies.
S
olve
(x
+ 3
)(x
- 2
) >
0.
Ste
p 1
D
eter
min
e w
hat
val
ues
of
x w
ill
mak
e th
e le
ft s
ide
0. I
n o
ther
w
ords
, wh
at v
alu
es o
f x
wil
l m
ake
eith
er x
+ 3
= 0
or
x -
2 =
0?
x
= -
3 or
2
Ste
p 2
P
lot
thes
e po
ints
on
a n
um
ber
lin
e. A
bove
th
e n
um
ber
lin
e, p
lace
a
+ i
f x
+ 3
is
posi
tive
for
th
at r
egio
n o
r a
- i
f x
+ 3
is
neg
ativ
e fo
r th
at r
egio
n. N
ext,
abo
ve t
he
sign
s yo
u h
ave
just
en
tere
d; d
o th
e sa
me
for
x –
2.
Ste
p 3
B
elow
th
e ch
art,
en
ter
the
prod
uct
of
the
two
sign
s. Y
our
sign
ch
art
shou
ld l
ook
like
th
e fo
llow
ing:
56
-6
43
21
0-
1-
5-4-
3-2
x -
2
x +
3
( x -
2)(
x +
3)
Th
e fi
nal
pos
itiv
e re
gion
s co
rres
pon
d to
val
ues
for
wh
ich
th
e qu
adra
tic
expr
essi
on i
s gr
eate
r th
an 0
. S
o, t
he
answ
er i
s
x
< -
3 or
x >
2.
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
1. (x
- 1
)(x
+ 2
) > 0
2.
(x +
5)(
x +
2) >
0
x
< -
2 o
r x >
1
x
< -
5 o
r x
> -
2
3. (x
- 1
)(x
- 5
) < 0
4.
(x +
2)(
x -
4) ≤
0
1
< x
< 5
-
2 ≤
x ≤
4
5. (x
– 3
)(x
+ 2
) ≥ 0
6.
(x +
3)(
x -
4) ≤
0x ≤
-2
or
x ≥
3
-3
≤ x
≤ 4
5-2
Exam
ple
013_
022_
ALG
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 5-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
17
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
So
lvin
g M
ult
i-S
tep
In
eq
ualiti
es
Solv
e M
ult
i-St
ep In
equ
alit
ies
To
solv
e li
nea
r in
equ
alit
ies
invo
lvin
g m
ore
than
on
e op
erat
ion
, un
do t
he
oper
atio
ns
in r
ever
se o
f th
e or
der
of o
pera
tion
s, ju
st a
s yo
u w
ould
sol
ve
an e
quat
ion
wit
h m
ore
than
on
e op
erat
ion
.
S
olve
6x
- 4
≤ 2
x +
12.
6x -
4 ≤
2x
+ 1
2 O
rigin
al in
equalit
y
6x -
4 -
2x
≤ 2
x +
12
- 2
x Su
btr
act
2x
from
each s
ide.
4x -
4 ≤
12
Sim
plif
y.
4x -
4 +
4 ≤
12
+ 4
A
dd 4
to e
ach s
ide.
4x ≤
16
Sim
plif
y.
4x
−
4 ≤
16
−
4
Div
ide e
ach s
ide b
y 4
.
x ≤
4
Sim
plif
y.
Th
e so
luti
on i
s {x
� x
≤ 4
}.
S
olve
3a
- 1
5 >
4 +
5a
.
3a -
15
> 4
+ 5
a O
rigin
al in
equalit
y
3a -
15
- 5
a >
4 +
5a
- 5
a Su
btr
act
5a
from
each s
ide.
-2a
- 1
5 >
4
Sim
plif
y.
-2a
- 1
5 +
15
> 4
+ 1
5 A
dd 1
5 t
o e
ach s
ide.
-2a
> 1
9 S
implif
y.
-2a
−
-2 <
19
−
-2
Div
ide e
ach s
ide b
y -
2
and c
hange >
to <
.
a <
-9
1 −
2
Sim
plif
y.
Th
e so
luti
on i
s {a
� a
< -
9 1 −
2 } .
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
Ch
eck
you
r so
luti
on.
1. 1
1y +
13
≥ -
1 2.
8n
- 1
0 <
6 -
2n
3.
q −
7 +
1 >
-5
{y
� y
≥ -
1 3
−
11 }
{n �
n <
1 3 −
5 }
{q
� q
> -
42}
4. 6
n +
12
< 8
+ 8
n
5. -
12 -
d >
-12
+ 4
d
6. 5
r -
6 >
8r
- 1
8
{
n �
n >
2}
{d
� d
< 0
} {
r � r
< 4
}
7.
-3x
+ 6
−
2 ≤
12
8. 7
.3y
- 1
4.4
> 4
.9y
9. -
8m -
3 <
18
- m
{
x �
x ≥
-6}
{
y �
y >
6}
{m
� m
> -
3}
10. -
4y -
10
> 1
9 -
2y
11. 9
n -
24n
+ 4
5 >
0
12.
4x -
2
−
5 ≥
-4
{y
� y
< -
14 1 −
2 }
{n
� n
< 3
} {x
� x
≥ -
4 1 −
2 }
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k y
our
solu
tion
. 13
–15.
Sam
ple
an
swer
: L
et n
= t
he
nu
mb
er.
13. N
egat
ive
thre
e ti
mes
a n
um
ber
plu
s fo
ur
is n
o m
ore
than
th
e n
um
ber
min
us
eigh
t.
-3n
+ 4
≤ n
- 8
; {n
� n
≥ 3
}
14. O
ne
fou
rth
of
a n
um
ber
decr
ease
d by
th
ree
is a
t le
ast
two.
1 −
4 n
- 3
≥ 2
; {n
� n
≥ 2
0}
15. T
he
sum
of
twel
ve a
nd
a n
um
ber
is n
o gr
eate
r th
an t
he
sum
of
twic
e th
e n
um
ber
and
-8.
1
2 +
n ≤
2n
+ (
-8)
; {n
� n
≥ 2
0}
5-3
Exam
ple
1Ex
amp
le 2
013_
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Answers (Lesson 5-2 and Lesson 5-3)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A7A01_A12_ALG1_A_CRM_C05_AN_661384.indd A7 12/21/10 6:15 PM12/21/10 6:15 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 5 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
18
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
So
lvin
g M
ult
i-S
tep
In
eq
ualiti
es
Solv
e In
equ
alit
ies
Invo
lvin
g t
he
Dis
trib
uti
ve P
rop
erty
Wh
en s
olvi
ng
ineq
ual
itie
s th
at c
onta
in g
rou
pin
g sy
mbo
ls, f
irst
use
th
e D
istr
ibu
tive
Pro
pert
y to
rem
ove
the
grou
pin
g sy
mbo
ls. T
hen
un
do t
he
oper
atio
ns
in r
ever
se o
f th
e or
der
of o
pera
tion
s, ju
st a
s yo
u
wou
ld s
olve
an
equ
atio
n w
ith
mor
e th
an o
ne
oper
atio
n.
S
olve
3a
- 2
(6a
- 4
) >
4 -
(4a
+ 6
).
3a -
2(6
a -
4)
> 4
- (
4a +
6)
Ori
gin
al in
equalit
y
3a -
12a
+ 8
> 4
- 4
a -
6
Dis
trib
utive
Pro
pert
y
-9a
+ 8
> -
2 -
4a
Com
bin
e lik
e t
erm
s.
-9a
+ 8
+ 4
a >
-2
- 4
a +
4a
Add 4
a to
each s
ide.
-5a
+ 8
> -
2 C
om
bin
e lik
e t
erm
s.
-5a
+ 8
- 8
> -
2 -
8
Subtr
act
8 f
rom
each s
ide.
-5a
> -
10
Sim
plif
y.
a <
2
Div
ide e
ach s
ide b
y -
5 a
nd c
hange >
to <
.
Th
e so
luti
on i
n s
et-b
uil
der
not
atio
n i
s {a
� a
< 2
}.
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
Ch
eck
you
r so
luti
on.
1. 2
(t +
3)
≥ 1
6 2.
3(d
- 2
) -
2d
> 1
6 3.
4h
- 8
< 2
(h -
1)
{
t � t
≥ 5
} {
d �
d >
22}
{
h �
h <
3}
4. 6
y +
10
> 8
- (
y +
14)
5.
4.6
(x -
3.4
) >
5.1
x 6.
-5x
- (
2x +
3)
≥ 1
{
y �
y >
-2
2 −
7 }
{x
� x
< -
31.2
8}
{x
� x
≤ -
4 −
7 }
7. 3
(2y
- 4
) -
2(y
+ 1
) >
10
8. 8
- 2
(b +
1)
< 1
2 -
3b
9. -
2(k
- 1
) >
8(1
+ k
)
{
y �
y >
6}
{b
� b
< 6
} {
k �
k <
- 3 −
5 }
10. 0
.3(y
- 2
) >
0.4
(1 +
y)
11. m
+ 1
7 ≤
-(4
m -
13)
{
y �
y <
-10
} {m
� m
≤ -
4 −
5 }
12. 3
n +
8 ≤
2(n
- 4
) -
2(1
- n
) 13
. 2(y
- 2
) >
-4
+ 2
y
{
n �
n ≥
18}
�
14. k
- 1
7 ≤
-(1
7 -
k)
15. n
- 4
≤ -
3(2
+ n
)
{
k �
k is
a r
eal n
um
ber
} {
n �
n ≤
- 1 −
2 }
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k y
our
solu
tion
.
16. T
wic
e th
e su
m o
f a
nu
mbe
r an
d 4
is l
ess
than
12.
2(n
+ 4
) <
12;
{n
� n
< 2
}
17. T
hre
e ti
mes
th
e su
m o
f a
nu
mbe
r an
d si
x is
gre
ater
th
an f
our
tim
es t
he
nu
mbe
r de
crea
sed
by t
wo.
18. T
wic
e th
e di
ffer
ence
of
a n
um
ber
and
fou
r is
les
s th
an t
he
sum
of
the
nu
mbe
r an
d fi
ve.
5-3
Exam
ple
16–1
8. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
3(n
+ 6
) >
4n
- 2
; {n
� n
< 2
0}
2(n
- 4
) <
n +
5;
{n �
n <
13}
013_
022_
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M_C
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R_6
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 5-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
19
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceS
olv
ing
Mu
lti-
Ste
p I
neq
ualiti
es
Ju
stif
y ea
ch i
nd
icat
ed s
tep
.
1.
3 −
4 t
- 3
≥ -
15
3 −
4 t
- 3
+ 3
≥ -
15 +
3
a.
?
3 −
4 t
≥ -
12
4 −
3 ( 3
−
4 ) t ≥
4 −
3 (-
12)
b.
?
t ≥
-16
a. A
dd
3 t
o e
ach
sid
e. b
. Mu
ltip
ly e
ach
sid
e by
4 −
3 .
2. 5
(k +
8)
- 7
≤ 2
3 5
k +
40
- 7
≤ 2
3 a.
?
5k +
33
≤ 2
35k
+ 3
3 -
33
≤ 2
3 -
33
b.
?5k
≤ -
10 5k
−
5
≤ -
10
−
5
c.
?
k ≤
-2
a. D
istr
ibu
tive
Pro
per
ty b
. Su
btr
act
33 f
rom
eac
h s
ide.
c. D
ivid
e ea
ch s
ide
by 5
.
Sol
ve e
ach
in
equ
alit
y. C
hec
k y
our
solu
tion
.
3. -
2b +
4 >
-6
4. 3
x +
15
≤ 2
1 5.
d
−
2 - 1
≥ 3
{
b �
b <
5}
{x
� x
≤ 2
} {
d �
d ≥
8}
6.
2 −
5 a
- 4
< 2
7.
- t −
5 +
7 >
-4
8. 3 −
4 j
- 1
0 ≥
5
{
a �
a <
15}
{
t � t
< 5
5}
{j
� j ≥
20}
9. -
2 −
3 f
+ 3
< -
9 10
. 2p
+ 5
≥ 3
p -
10
11. 4
k +
15
> -
2k +
3
{
f � f
> 1
8}
{p
� p
≤ 1
5}
{k
� k
> -
2}
12. 2
(-3m
- 5
) ≥
-28
13
. -6(
w +
1)
< 2
(w +
5)
14. 2
(q -
3)
+ 6
≤ -
10
{
m �
m ≤
3}
{w
� w
> -
2}
{q
� q
≤ -
5}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m.
Ch
eck
you
r so
luti
on.
15–2
0. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
. 15
. Fou
r m
ore
than
th
e qu
otie
nt
of a
nu
mbe
r an
d th
ree
is a
t le
ast
nin
e.
n
−
3 + 4
≥ 9
;
{n
� n
≥ 1
5} 16
. Th
e su
m o
f a
nu
mbe
r an
d fo
urt
een
is
less
th
an o
r eq
ual
to
thre
e ti
mes
th
e n
um
ber.
n
+ 1
4 ≤
3n
; {n
� n
≥ 7
} 17
. Neg
ativ
e th
ree
tim
es a
nu
mbe
r in
crea
sed
by s
even
is
less
th
an n
egat
ive
elev
en.
-
3n +
7 <
-11
; {n
� n
> 6
} 18
. Fiv
e ti
mes
a n
um
ber
decr
ease
d by
eig
ht
is a
t m
ost
ten
mor
e th
an t
wic
e th
e n
um
ber.
5
n -
8 ≤
2n
+ 1
0; {
n �
n ≤
6}
19. S
even
mor
e th
an f
ive
sixt
hs
of a
nu
mbe
r is
mor
e th
an n
egat
ive
thre
e.
5 −
6 n
+ 7
> -
3;
{
n �
n >
-12
} 20
. Fou
r ti
mes
th
e su
m o
f a
nu
mbe
r an
d tw
o in
crea
sed
by t
hre
e is
at
leas
t tw
enty
-sev
en.
4
(n +
2)
+ 3
≥ 2
7; {
n �
n ≥
4}
5-3
013_
022_
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4:37
PM
Answers (Lesson 5-3)
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ight
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Chapter 5 A9 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
20
Gle
ncoe
Alg
ebra
1
Prac
tice
So
lvin
g M
ult
i-S
tep
In
eq
ualiti
es
Ju
stif
y ea
ch i
nd
icat
ed s
tep
. 1
. x
> 5x
- 1
2 −
8
8x >
(8)
5x -
12
−
8
a.
?
8x >
5x
- 1
2
8x -
5x
> 5
x -
12
- 5
x b
. ?
3x >
-12
3x
−
3 >
-12
−
3
c.
?
x >
-4
a. M
ult
iply
eac
h s
ide
by 8
. b
. Su
btr
act
5x f
rom
eac
h s
ide.
c. D
ivid
e ea
ch s
ide
by 3
.
2.
2(2h
+ 2
) <
2(3
h +
5)
- 1
24h
+ 4
< 6
h +
10
- 1
2 a.
?
4h +
4 <
6h
- 2
4h +
4 -
6h
< 6
h -
2 -
6h
b
. ?
-2h
+ 4
< -
2-
2h +
4 -
4 <
-2
- 4
c.
?
-2h
< -
6
-2h
−
-2
> -
6 −
-
2 d
. ?
h >
3 a
. Dis
trib
uti
ve P
rop
erty
b. S
ub
trac
t 6h
fro
m e
ach
sid
e. c
. Su
btr
act
4 fr
om
eac
h s
ide.
d. D
ivid
e ea
ch s
ide
by -
2 an
d
chan
ge
< t
o >
.
Sol
ve e
ach
in
equ
alit
y. C
hec
k y
our
solu
tion
.
3. -
5 -
t −
6 ≥
-9
4. 4
u -
6 ≥
6u
- 2
0 5.
13
> 2 −
3 a
- 1
{
t � t
≤ 2
4}
{u
� u
≤ 7
} {
a �
a <
21}
6.
w +
3
−
2
< -
8 {w
� w
< -
19}
7. 3f
- 1
0 −
5
>
7 {
f � f
> 1
5}
8. h
≤
6h +
3
−
5 {
h �
h ≥
-3}
9.
3(z
+ 1
) +
11
< -
2(z
+ 1
3) {
z �
z <
-8}
10. 3
r +
2(4
r +
2)
≤ 2
(6r
+ 1
) {r
� r
≥ 2
} 11
. 5n
- 3
(n -
6)
≥ 0
{n
� n
≥ -
9}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k y
our
solu
tion
.
12. A
nu
mbe
r is
les
s th
an o
ne
fou
rth
th
e su
m o
f th
ree
tim
es t
he
nu
mbe
r an
d fo
ur.
n
< 3n
+ 4
−
4 ;
{n �
n <
4}
13. T
wo
tim
es t
he
sum
of
a n
um
ber
and
fou
r is
no
mor
e th
an t
hre
e ti
mes
th
e su
m o
f th
e n
um
ber
and
seve
n d
ecre
ased
by
fou
r.
14. G
EOM
ETRY
Th
e ar
ea o
f a
tria
ngu
lar
gard
en c
an b
e n
o m
ore
than
120
squ
are
feet
. Th
e ba
se o
f th
e tr
ian
gle
is 1
6 fe
et. W
hat
is
the
hei
ght
of t
he
tria
ngl
e?
15. M
USI
C P
RA
CTI
CE
Nab
uko
pra
ctic
es t
he
viol
in a
t le
ast
12 h
ours
per
wee
k. S
he
prac
tice
s fo
r th
ree
fou
rth
s of
an
hou
r ea
ch s
essi
on. I
f N
abu
ko h
as a
lrea
dy p
ract
iced
3
hou
rs i
n o
ne
wee
k, h
ow m
any
sess
ion
s re
mai
n t
o m
eet
or e
xcee
d h
er w
eekl
y pr
acti
ce g
oal?
5-3
12–1
3. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
2(n
+ 4
) ≤
3(n
+ 7
) -
4;
{n �
n ≥
-9}
no
mo
re t
han
15
ft
at le
ast
12 s
essi
on
s
013_
022_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 5-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
21
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
So
lvin
g M
ult
i-S
tep
In
eq
ualiti
es
1.B
EAC
HC
OM
BIN
G J
ay h
as l
ost
his
m
oth
er’s
fav
orit
e n
eckl
ace,
so
he
wil
l re
nt
a m
etal
det
ecto
r to
try
to
fin
d it
. A
ren
tal
com
pan
y ch
arge
s a
one-
tim
e re
nta
l fe
e of
$15
plu
s $2
per
hou
r to
ren
t a
met
al d
etec
tor.
Jay
has
on
ly $
35 t
o sp
end.
Wh
at i
s th
e m
axim
um
am
oun
t of
ti
me
he
can
ren
t th
e m
etal
det
ecto
r?
10 h
ou
rs
2.A
GES
Bob
by, B
illy
, an
d B
arry
Sm
ith
are
ea
ch o
ne
year
apa
rt i
n a
ge. T
he
sum
of
thei
r ag
es i
s gr
eate
r th
an t
he
age
of t
hei
r fa
ther
, wh
o is
60.
How
old
can
th
e ol
dest
br
oth
er c
an b
e?
no
yo
un
ger
th
an 2
2
3.TA
XI
FAR
E Ja
mal
wor
ks i
n a
cit
y an
d so
met
imes
tak
es a
tax
i to
wor
k. T
he
taxi
cabs
ch
arge
$1.
50 f
or t
he
firs
t 1 − 5
mil
e
and
$0.2
5 fo
r ea
ch a
ddit
ion
al 1 − 5
mil
e.
Jam
al h
as o
nly
$3.
75 i
n h
is p
ocke
t. W
hat
is
th
e m
axim
um
dis
tan
ce h
e ca
n t
rave
l by
tax
i if
he
does
not
tip
th
e dr
iver
?
2 m
i
4.PL
AY
GR
OU
ND
Th
e pe
rim
eter
of
a re
ctan
gula
r pl
aygr
oun
d m
ust
be
no
grea
ter
than
120
met
ers,
bec
ause
th
at i
s th
e to
tal
len
gth
of
the
mat
eria
ls
avai
labl
e fo
r th
e bo
rder
. Th
e w
idth
of
the
play
grou
nd
can
not
exc
eed
22 m
eter
s.
Wh
at a
re t
he
poss
ible
len
gth
s of
th
e pl
aygr
oun
d?
less
th
an o
r eq
ual
to
38
met
ers
5. M
EDIC
INE
Cla
rk’s
Ru
le i
s a
form
ula
u
sed
to d
eter
min
e pe
diat
ric
dosa
ges
of
over
-th
e-co
un
ter
med
icin
es.
w
eigh
t of
ch
ild
( lb)
−
15
0
× a
dult
dos
e =
chi
ld
dose
a. I
f an
adu
lt d
ose
of a
ceta
min
oph
en i
s 10
00 m
illi
gram
s an
d a
chil
d w
eigh
s n
o m
ore
than
90
pou
nds
, wh
at i
s th
e re
com
men
ded
chil
d’s
dose
?
x ≤
60
0; n
o m
ore
th
an 6
00
mg
b.
Th
is l
abel
app
ears
on
a c
hil
d’s
cold
m
edic
ine.
Wh
at i
s th
e ad
ult
min
imu
m
dosa
ge i
n m
illi
lite
rs?
Wei
gh
t (l
b)
Ag
e (y
r)D
ose
un
de
r 4
8u
nd
er
6ca
ll a
do
cto
r
48
-95
6-1
12
tsp
or
10
mL
15
.79
mL
c. W
hat
is
the
max
imu
m a
dult
dos
age
in
mil
lili
ters
?
31.2
5 m
L
5-3
013_
022_
ALG
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M_C
05_C
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Answers (Lesson 5-3)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A9A01_A12_ALG1_A_CRM_C05_AN_661384.indd A9 12/21/10 6:15 PM12/21/10 6:15 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 5 A10 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
22
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Carl
os M
on
tezu
ma
Du
rin
g h
is l
ifet
ime,
Car
los
Mon
tezu
ma
(186
6–19
23)
was
on
e of
th
e m
ost
infl
uen
tial
Nat
ive
Am
eric
ans
in t
he
Un
ited
Sta
tes.
He
was
re
cogn
ized
as
a pr
omin
ent
phys
icia
n a
nd
was
als
o a
pass
ion
ate
advo
cate
of
th
e ri
ghts
of
Nat
ive
Am
eric
an p
eopl
es. T
he
exer
cise
s th
at f
ollo
w w
ill
hel
p yo
u l
earn
som
e in
tere
stin
g fa
cts
abou
t D
r. M
onte
zum
a’s
life
.
Sol
ve e
ach
in
equ
alit
y. T
he
wor
d o
r p
hra
se n
ext
to t
he
equ
ival
ent
ineq
ual
ity
wil
l co
mp
lete
th
e st
atem
ent
corr
ectl
y.
1. -
2k >
10
2. 5
≥ r
- 9
Mon
tezu
ma
was
bor
n i
n t
he
stat
e
He
was
a N
ativ
e A
mer
ican
of
the
of
? .
Yav
apai
s, w
ho
are
a ?
peo
ple.
a. k
< -
5 A
rizo
na
a. r
≤ -
4 N
avaj
o
b.
k >
-5
Mon
tan
a b
. r
≥ -
4 M
ohaw
k
c. k
> 1
2 U
tah
c.
r ≤
14
Moh
ave-
Apa
che
3. -
y ≤
-9
4. -
3 +
q >
12
M
onte
zum
a re
ceiv
ed a
med
ical
A
s a
phys
icia
n, M
onte
zum
a’s
fiel
d of
de
gree
fro
m
? i
n 1
889.
s
peci
aliz
atio
n w
as
? .
a. y
≥ 9
C
hic
ago
Med
ical
Col
lege
a.
q >
-4
hea
rt s
urg
ery
b.
y ≥
-9
Har
vard
Med
ical
Sch
ool
b.
q >
15
inte
rnal
med
icin
e
c. y
≤ 9
Jo
hn
s H
opki
ns
Un
iver
sity
c.
q <
-15
re
spir
ator
y di
seas
es
5. 5
+ 4
x -
14
≤ x
6.
7 -
t <
7 +
t
F
or m
uch
of
his
car
eer,
he
mai
nta
ined
I
n a
ddit
ion
to
mai
nta
inin
g h
is m
edic
ala
med
ical
pra
ctic
e in
?
. p
ract
ice,
he
was
als
o a(
n)
?.
a. x
≤ 9
N
ew Y
ork
Cit
y a.
t >
7
dire
ctor
of
a bl
ood
ban
k
b.
x ≤
3
Ch
icag
o b
. t
> 0
in
stru
ctor
at
a m
edic
al c
olle
ge
c. x
≥ -
9 B
osto
n
c. t
< -
7 le
gal
cou
nse
l to
ph
ysic
ian
s
7. 3
a +
8 ≥
4a
- 1
0 8.
6n
> 8
n -
12
M
onte
zum
a fo
un
ded,
wro
te, a
nd
Mon
tezu
ma
test
ifie
d be
fore
a
edit
ed
?, a
mon
thly
new
slet
ter
com
mit
tee
of t
he
Un
ited
Sta
tes
that
add
ress
ed N
ativ
e A
mer
ican
C
ongr
ess
con
cern
ing
his
wor
k in
co
nce
rns.
t
reat
ing
?.
a. a
≤ -
2 Ya
vapa
i a.
n <
6
appe
ndi
citi
s
b.
a ≥
18
Apa
che
b.
n >
-6
asth
ma
c. a
≤ 1
8 W
assa
ja
c. n
> -
10
hea
rt a
ttac
ks
5-3
013_
022_
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1_A
_CR
M_C
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4.in
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10
4:37
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-4
Stud
y G
uide
and
Inte
rven
tion
So
lvin
g C
om
po
un
d I
neq
ualiti
es
Ineq
ual
itie
s C
on
tain
ing
an
d A
com
pou
nd
ineq
ual
ity
con
tain
ing
and
is
tru
e on
ly
if b
oth
in
equ
alit
ies
are
tru
e. T
he
grap
h o
f a
com
pou
nd
ineq
ual
ity
con
tain
ing
and
is
the
inte
rsec
tion
of
the
grap
hs
of t
he
two
ineq
ual
itie
s. E
very
sol
uti
on o
f th
e co
mpo
un
d in
equ
alit
y m
ust
be
a so
luti
on o
f bo
th i
neq
ual
itie
s.
G
rap
h t
he
solu
tion
se
t of
x <
2 a
nd
x ≥
-1.
G
raph x
< 2
.
G
raph x
≥ -
1.
F
ind t
he inte
rsection.
Th
e so
luti
on s
et i
s {x
� -
1 ≤
x <
2}.
S
olve
-1
< x
+ 2
< 3
. Th
en
grap
h t
he
solu
tion
set
.-
1 <
x +
2
and
x +
2 <
3-
1 -
2 <
x +
2 -
2
x
+ 2
- 2
< 3
- 2
-3
< x
x <
1
G
raph x
> -
3.
G
raph x
< 1
.
F
ind t
he inte
rsection.
Th
e so
luti
on s
et i
s {x
� -
3 <
x <
1}.
Exer
cise
sG
rap
h t
he
solu
tion
set
of
each
com
pou
nd
in
equ
alit
y.
1. b
> -
1 an
d b
≤ 3
2.
2 ≥
q ≥
-5
3. x
> -
3 an
d x
≤ 4
4. -
2 ≤
p <
4
5. -
3 <
d a
nd
d<
2
6. -
1 ≤
p ≤
3
Sol
ve e
ach
com
pou
nd
in
equ
alit
y. T
hen
gra
ph
th
e so
luti
on s
et.
7. 4
< w
+ 3
≤ 5
8.
-3
≤ p
- 5
< 2
{
w �
1 <
w ≤
2}
{p �
2 ≤
p <
7}
9. -
4 <
x +
2 ≤
-2
10. y
- 1
< 2
an
d y
+ 2
≥ 1
{
x �
-6
< x
≤ -
4}
{y �
-1
≤ y
< 3
}
11. n
- 2
> -
3 an
d n
+ 4
< 6
12
. d -
3 <
6d
+ 1
2 <
2d
+ 3
2
{
n �
-1
< n
< 2
} {d
� -
3 <
d <
5}
-2
-1
-3
01
23
-3
-2
-1
01
23
-3
-2
-1
01
23
-3
-2
-1
01
23
45
-3
-4
-2
-1
01
23
4
-3
-4
-2
-1
01
23
4-
7-
6-
5-
4-
3-
2-
10
1
01
23
45
67
8-
3-
4-
2-
10
12
34
-3
-4
-2
-1
01
23
4-
3-
4-
2-
10
12
34
-3
-2
-1
01
23
45
-4
-3
-2
-1
01
23
4-
4-
3-
6-
5-
2-
10
12
-4
-3
-2
-1
01
23
4
-2
-1
-4
-3
01
2
-3
-4
-2
-1
01
2
-3
-4
-2
-1
01
2
5-4
Cha
pte
r 5
23
Gle
ncoe
Alg
ebra
1
Exam
ple
1Ex
amp
le 2
023_
042_
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M_C
05_C
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4.in
dd
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4:37
PM
Answers (Lesson 5-3 and Lesson 5-4)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A10A01_A12_ALG1_A_CRM_C05_AN_661384.indd A10 12/21/10 6:15 PM12/21/10 6:15 PM
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anie
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Chapter 5 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
24
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
So
lvin
g C
om
po
un
d I
neq
ualiti
es
Ineq
ual
itie
s C
on
tain
ing
or
A c
ompo
un
d in
equ
alit
y co
nta
inin
g or
is
tru
e if
on
e or
bo
th o
f th
e in
equ
alit
ies
are
tru
e. T
he
grap
h o
f a
com
pou
nd
ineq
ual
ity
con
tain
ing
or i
s th
e u
nio
n o
f th
e gr
aph
s of
th
e tw
o in
equ
alit
ies.
Th
e u
nio
n c
an b
e fo
un
d by
gra
phin
g bo
th
ineq
ual
itie
s on
th
e sa
me
nu
mbe
r li
ne.
A s
olu
tion
of
the
com
pou
nd
ineq
ual
ity
is a
sol
uti
on o
f ei
ther
in
equ
alit
y, n
ot n
eces
sari
ly b
oth
.
S
olve
2a
+ 1
< 1
1 or
a >
3a
+ 2
. Th
en g
rap
h t
he
solu
tion
set
.
2a
+ 1
< 1
1 or
a
> 3
a +
2 2
a +
1 -
1 <
11
- 1
a -
3a
> 3
a -
3a
+ 2
2a
< 1
0
-2a
> 2
2a
−
2
< 10
−
2
-
2a
−
-2
<
2 −
-2
a
< 5
a <
-1
-2
-1
01
23
45
6
Gra
ph a
< 5
.
-2
-1
01
23
45
6
Gra
ph a
< -
1.
-2
-1
01
23
45
6
Fin
d t
he u
nio
n.
Th
e so
luti
on s
et i
s {a
� a
< 5
}.
Exer
cise
sG
rap
h t
he
solu
tion
set
of
each
com
pou
nd
in
equ
alit
y. 1
. b >
2 o
r b
≤ -
3 2.
3 ≥
q o
r q
≤ 1
3.
y ≤
-4
or y
> 0
4. 4
≤ p
or
p <
8
5. -
3 <
d o
r d
< 2
6.
-2
≤ x
or
3 ≤
x
Sol
ve e
ach
com
pou
nd
in
equ
alit
y. T
hen
gra
ph
th
e so
luti
on s
et.
7. 3
< 3
w o
r 3w
≥ 9
8.
-3p
+ 1
≤-
11 o
r p
< 2
{
w �
1 <
w}
{p
� p
≥ 4
or
p <
2}
9. 2
x +
4 ≤
6 o
r x
≥ 2
x -
4
10. 2
y +
2 <
12
or y
- 3
≥ 2
y
{
x �
x ≤
4}
{y
� y
< 5
}
11.
1 −
2 n
> -
2 or
2n
- 2
< 6
+ n
12
. 3a
+ 2
≥ 5
or
7 +
3a
< 2
a +
6
{
n �
n is
a r
eal n
um
ber
}
{a �
a <
-1
or
a ≥
1}
0
-1
-2
-3
-4
12
34
0-
1-
2-
3-
41
23
4
01
23
45
67
8-
2-
10
12
34
56
01
23
45
67
8-
3-
4-
2-
10
12
34
-3
-4
-2
-1
01
23
40
-1
-2
-3
-4
12
34
0-
1-
21
23
45
6
-3
-4
-5
-2
-1
01
23
-3
-4
-2
-1
01
23
4-
3-
4-
2-
10
12
34
5-4
Exam
ple
023_
042_
ALG
1_A
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M_C
05_C
R_6
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4.in
dd
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4:37
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-4
Cha
pte
r 5
25
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceS
olv
ing
Co
mp
ou
nd
In
eq
ualiti
es
Gra
ph
th
e so
luti
on s
et o
f ea
ch c
omp
oun
d i
neq
ual
ity.
1. b
> 3
or
b ≤
0
2. z
≤ 3
an
d z
≥ -
2
3. k
> 1
an
d k
> 5
4.
y <
-1
or y
≥ 1
Wri
te a
com
pou
nd
in
equ
alit
y fo
r ea
ch g
rap
h.
5.
-2
-1
-4
-3
01
23
4
6.
-
3 <
x ≤
3
1
≤ x
≤ 4
7.
8.
x
< -
2 o
r x ≥
1
x <
-1
or
x >
2
Sol
ve e
ach
com
pou
nd
in
equ
alit
y. T
hen
gra
ph
th
e so
luti
on s
et.
9. m
+ 3
≥ 5
an
d m
+ 3
< 7
10
. y -
5 <
-4
or y
- 5
≥ 1
{
m �
2 ≤
m <
4}
{y
� y
< 1
or
y ≥
6}
11. 4
< f
+ 6
an
d f
+ 6
< 5
12
. w +
3 ≤
0 o
r w
+ 7
≥ 9
{
f �
-2
< f
< -
1}
{w
� w
≤ -
3 o
r w
≥ 2
}
13. -
6 <
b -
4 <
2
14. p
- 2
≤ -
2 or
p -
2 >
1
{
b �
-2
< b
< 6
}
{p �
p ≤
0 o
r p
> 3
}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m.
Ch
eck
you
r so
luti
on.
15-
17. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
15. A
nu
mbe
r pl
us
one
is g
reat
er t
han
neg
ativ
e fi
ve a
nd
less
th
an t
hre
e.
-5
< n
+ 1
< 3
; {n
� -
6 <
n <
2}
16. A
nu
mbe
r de
crea
sed
by t
wo
is a
t m
ost
fou
r or
at
leas
t n
ine.
n
- 2
≤ 4
or
n -
2 ≥
9;
{n �
n ≤
6 o
r n
≥ 1
1}
17. T
he
sum
of
a n
um
ber
and
thre
e is
no
mor
e th
an e
igh
t or
is
mor
e th
an t
wel
ve.
n
+ 3
≤ 8
or
n +
3 >
12;
{n
� n
≤ 5
or
n >
9}
-3
-4
-2
-1
01
23
4-
2-
10
12
34
56
-3
-4
-2
-1
01
23
4-
4-
3-
2-
10
12
34
-2
-1
01
23
45
6-
2-
10
12
34
56
-4
-3
-2
-1
01
23
4
-3
-4
-2
-1
01
23
4
-4
-3
-2
-1
01
23
4-
3-
4-
2-
10
12
34
-2
-1
01
23
45
6
-4
-3
-2
-1
01
23
4
5-4 0
12
34
56
78
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
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4.in
dd
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/21/
10
4:37
PM
Answers (Lesson 5-4)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A11A01_A12_ALG1_A_CRM_C05_AN_661384.indd A11 12/21/10 6:15 PM12/21/10 6:15 PM
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 5 A12 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
26
Gle
ncoe
Alg
ebra
1
Prac
tice
So
lvin
g C
om
po
un
d I
neq
ualiti
es
Gra
ph
th
e so
luti
on s
et o
f ea
ch c
omp
oun
d i
neq
ual
ity.
1. -
4 ≤
n ≤
1
2. x
> 0
or
x <
3
3. g
< -
3 or
g ≥
4
4. -
4 ≤
p ≤
4
Wri
te a
com
pou
nd
in
equ
alit
y fo
r ea
ch g
rap
h.
5.
6.
x
≤ -
3 o
r x ≥
3
x <
2 o
r x ≥
3
7.
8.
0
≤ x
< 5
-5
< x
< 0
Sol
ve e
ach
com
pou
nd
in
equ
alit
y. T
hen
gra
ph
th
e so
luti
on s
et.
9. k
- 3
< -
7 or
k +
5 ≥
8
10. -
n <
2 o
r 2n
- 3
> 5
{
k �
k <
-4
or
k ≥
3}
{n
� n
> -
2}
11. 5
< 3
h +
2 ≤
11
12. 2
c -
4 >
-6
and
3c +
1 <
13
{
h �
1 <
h ≤
3}
{c
� -
1 <
c <
4}
Def
ine
a va
riab
le, w
rite
an
in
equ
alit
y, a
nd
sol
ve e
ach
pro
ble
m. C
hec
k
you
r so
luti
on.
13-
14. S
amp
le a
nsw
er:
Let
n =
th
e n
um
ber
.
13. T
wo
tim
es a
nu
mbe
r pl
us
one
is g
reat
er t
han
fiv
e an
d le
ss t
han
sev
en.
5
< 2
n +
1 <
7;
{n �
2 <
n <
3}
14. A
nu
mbe
r m
inu
s on
e is
at
mos
t n
ine,
or
two
tim
es t
he
nu
mbe
r is
at
leas
t tw
enty
-fou
r.
n -
1 ≤
9 o
r 2n
≥ 2
4; {
n �
n ≤
10
or
n ≥
12}
15. M
ETEO
RO
LOG
Y S
tron
g w
inds
cal
led
the
prev
aili
ng
wes
terl
ies
blow
fro
m w
est
to e
ast
in a
bel
t fr
om 4
0° t
o 60
° la
titu
de i
n b
oth
th
e N
orth
ern
an
d S
outh
ern
Hem
isph
eres
.
a
. Wri
te a
n i
neq
ual
ity
to r
epre
sen
t th
e la
titu
de o
f th
e pr
evai
lin
g w
este
rlie
s.
{w
� 4
0 ≤
w ≤
60}
b
. Wri
te a
n i
neq
ual
ity
to r
epre
sen
t th
e la
titu
des
wh
ere
the
prev
aili
ng
wes
terl
ies
are
n
ot l
ocat
ed.
16. N
UTR
ITIO
N A
coo
kie
con
tain
s 9
gram
s of
fat
. If
you
eat
no
few
er t
han
4 a
nd
no
mor
e th
an 7
coo
kies
, how
man
y gr
ams
of f
at w
ill
you
con
sum
e?
-3
-4
-2
-1
01
23
4
-2
-1
-4
-3
-6
-5
01
2
-2
-1
01
23
45
6-
2-
1-
4-
30
12
34
-4
-3
-2
-1
01
23
4-
3-
4-
2-
10
12
34
-2
-3
-4
-5
-6
-1
01
2-
2-
10
12
34
56
-2
-1
01
23
45
6-
4-
3-
2-
10
12
34
-2
-1
-4
-3
01
23
4
0-
1-
2-
3-
41
23
4
5-4
{w �
w <
40
or
w >
60}
bet
wee
n 3
6 g
an
d 6
3 g
incl
usi
ve
023_
042_
ALG
1_A
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M_C
05_C
R_6
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4.in
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10
3:25
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-4
Cha
pte
r 5
27
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
So
lvin
g C
om
po
un
d I
neq
ualiti
es
1. W
EATH
ER K
en s
aw t
his
gra
ph i
n t
he
new
spap
er w
eath
er f
orec
ast.
It
show
s th
e pr
edic
ted
tem
pera
ture
ran
ge f
or t
he
foll
owin
g da
y. W
rite
an
in
equ
alit
y to
re
pres
ent
the
nu
mbe
r li
ne
grap
h.
2. P
OO
LS T
he
pH o
f a
pers
on’s
eye
s is
7.2
. T
her
efor
e, t
he
idea
l pH
for
th
e w
ater
in
a
swim
min
g po
ol i
s be
twee
n 7
.0 a
nd
7.6.
W
rite
a c
ompo
un
d in
equ
alit
y to
re
pres
ent
pH l
evel
s th
at c
ould
cau
se
phys
ical
dis
com
fort
to
a pe
rson
’s e
yes.
x
≤ 7
.0 o
r x
≥7.
6
3. S
TOR
E SI
GN
S In
Ran
dy’s
tow
n,
stre
et-s
ide
sign
s th
emse
lves
mu
st b
e ex
actl
y 8
feet
hig
h. W
hen
mou
nte
d on
po
les,
th
e si
gns
mu
st b
e sh
orte
r th
an
20 f
eet
or t
alle
r th
an 3
5 fe
et s
o th
at
they
do
not
in
terf
ere
wit
h t
he
pow
er
and
phon
e li
nes
. Wri
te a
com
pou
nd
ineq
ual
ity
to r
epre
sen
t th
e po
ssib
le
hei
ght
of t
he
pole
s.
4. H
EALT
H T
he
hu
man
hea
rt c
ircu
late
s fr
om 7
70,0
00 t
o 1,
600,
000
gall
ons
of
bloo
d th
rou
gh a
per
son
’s b
ody
ever
y ye
ar.
How
man
y ga
llon
s of
blo
od d
oes
the
hea
rt c
ircu
late
th
rou
gh t
he
body
in
on
e da
y?
5. H
EALT
H B
ody
mas
s in
dex
(BM
I) i
s a
mea
sure
of
wei
ght
stat
us.
Th
e B
MI
of a
pe
rson
ove
r 20
yea
rs o
ld i
s ca
lcu
late
d u
sin
g th
e fo
llow
ing
form
ula
.
B
MI
= 7
03 ×
w
eigh
t in
pou
nds
−
−
(
hei
ght
in i
nch
es)2
T
he
tabl
e be
low
sh
ows
the
mea
nin
g of
di
ffer
ent
BM
I m
easu
res.
So
urce
: C
ente
rs f
or D
isea
se C
ontr
ol
a. W
rite
a c
ompo
un
d in
equ
alit
y to
re
pres
ent
the
nor
mal
BM
I ra
nge
.
18.5
≤ x
< 2
5
b.
Wri
te a
com
pou
nd
ineq
ual
ity
to
repr
esen
t an
adu
lt w
eigh
t th
at i
s w
ith
in t
he
hea
lth
y B
MI
ran
ge f
or a
pe
rson
6 f
eet
tall
.
136.
4 ≤
w ≤
183
.6
62°
64°
66°
68°
70°
60°
58°
56°
54°
52°
50°F
5-4
bet
wee
n 2
110
and
438
4 g
al
BM
IW
eig
ht
Sta
tus
less t
ha
n 1
8.5
un
de
rwe
igh
t
18
.5 –
24
.9n
orm
al
25
– 2
9.9
ove
rwe
igh
t
mo
re t
ha
n 3
0o
be
se
54 ≤
x ≤
68
x <
12
or
x >
27
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
2712
/21/
10
4:37
PM
Answers (Lesson 5-4)
A01_A12_ALG1_A_CRM_C05_AN_661384.indd A12A01_A12_ALG1_A_CRM_C05_AN_661384.indd A12 12/23/10 3:28 PM12/23/10 3:28 PM
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pyr
ight
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lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
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Chapter 5 A13 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
28
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
So
me P
rop
ert
ies o
f In
eq
ualiti
es
Th
e tw
o ex
pres
sion
s on
eit
her
sid
e of
an
in
equ
alit
y sy
mbo
l ar
e so
met
imes
cal
led
the
firs
t an
d se
con
d m
embe
rs o
f th
e in
equ
alit
y.
If t
he
ineq
ual
ity
sym
bols
of
two
ineq
ual
itie
s po
int
in t
he
sam
e di
rect
ion
, th
e in
equ
alit
ies
hav
e th
e sa
me
sen
se. F
or e
xam
ple,
a <
b
and
c <
d h
ave
the
sam
e se
nse
; a <
b a
nd
c >
d h
ave
oppo
site
sen
ses.
In t
he
prob
lem
s on
th
is p
age,
you
wil
l ex
plor
e so
me
prop
erti
es
of i
neq
ual
itie
s.
Th
ree
of t
he
fou
r st
atem
ents
bel
ow a
re t
rue
for
all
nu
mb
ers
a a
nd
b (
or a
, b, c
, an
d d
). W
rite
eac
h s
tate
men
t in
alg
ebra
ic
form
. If
the
stat
emen
t is
tru
e fo
r al
l n
um
ber
s, p
rove
it.
If
it i
s n
ot t
rue,
giv
e an
exa
mp
le t
o sh
ow t
hat
it
is f
alse
.
1. G
iven
an
in
equ
alit
y, a
new
an
d eq
uiv
alen
t in
equ
alit
y ca
n b
e cr
eate
d by
in
terc
han
gin
g th
e m
embe
rs a
nd
reve
rsin
g th
e se
nse
.
I
f a >
b, t
hen
b <
a.
a
> b
, a -
b >
0, -
b >
-a, (
-1)
(-b
) <
(-
1)(-
a),
b <
a
2. G
iven
an
in
equ
alit
y, a
new
an
d eq
uiv
alen
t in
equ
alit
y ca
n b
e cr
eate
d by
ch
angi
ng
the
sign
s of
bot
h t
erm
s an
d re
vers
ing
the
sen
se.
I
f a >
b, t
hen
-a <
-b
.
a >
b, a
- b
> 0
, -b
> -
a, -
a <
-b
3. G
iven
tw
o in
equ
alit
ies
wit
h t
he
sam
e se
nse
, th
e su
m o
f th
e co
rres
pon
din
g m
embe
rs a
re m
embe
rs o
f an
equ
ival
ent
ineq
ual
ity
wit
h t
he
sam
e se
nse
.
I
f a >
b a
nd
c >
d, t
hen
a +
c >
b +
d.
a
> b
an
d c
> d
, so
(a -
b)
and
(c -
d)
are
po
siti
ve n
um
ber
s,
so t
he
sum
(a -
b)
+ (
c -
d)
is a
lso
po
siti
ve.
(a -
b)
+ (c
- d
) >
0, s
o a
+ c
> b
+ d
.
4. G
iven
tw
o in
equ
alit
ies
wit
h t
he
sam
e se
nse
, th
e di
ffer
ence
of
the
corr
espo
ndi
ng
mem
bers
are
mem
bers
of
an e
quiv
alen
t in
equ
alit
y w
ith
th
e sa
me
sen
se.
I
f a >
b a
nd
c >
d, t
hen
a -
c >
b -
d. T
he
stat
emen
t is
fal
se. 5
> 4
an
d 3
> 2
, bu
t 5
- 3
≯ 4
- 2
.
5-4
023_
042_
ALG
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M_C
05_C
R_6
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4.in
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-5
Cha
pte
r 5
29
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
In
eq
ualiti
es I
nvo
lvin
g A
bso
lute
Valu
e
Ineq
ual
itie
s In
volv
ing
Ab
solu
te V
alu
e (<
) W
hen
so
lvin
g in
equ
alit
ies
that
in
volv
e ab
solu
te v
alu
e, t
her
e ar
e tw
o ca
ses
to c
onsi
der
for
ineq
ual
itie
s in
volv
ing
< (
or ≤
).
Rem
embe
r th
at i
neq
ual
itie
s w
ith
an
d a
re r
elat
ed t
o in
ters
ecti
ons.
S
olve
|3a
+ 4
| <
10.
Th
en g
rap
h t
he
solu
tion
set
.
Wri
te �
3a +
4 �
< 1
0 as
3a
+ 4
< 1
0 an
d 3a
+ 4
> -
10.
3a
+ 4
< 1
0 an
d 3a
+ 4
> -
10 3
a +
4 -
4 <
10
- 4
3a +
4 -
4 >
-10
- 4
3a
< 6
3a >
-14
3a
−
3
< 6 −
3
3a
−
3
> -
14
−
3
a
< 2
a >
-4
2 −
3
Th
e so
luti
on s
et i
s {a
� -
4 2 −
3 <
a <
2} .
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
Th
en g
rap
h t
he
solu
tion
set
.
1. �
y � <
3
2. �
x -
4 �
< 4
3.
� y
+ 3
� ≤
2
{
y �
-3
< y
< 3
} {
x �
0 <
x <
8}
{y
� -
5 ≤
y ≤
-1}
-3
-4
-2
-1
01
23
4
0
12
34
56
78
-8
-7
-6
-5
-4
-3
-2
-1
0
4. �
b +
2 � ≤
3
5. �
w -
2 �
≤ 5
6.
� t
+ 2
� ≤
4
{b �
-5
≤b
≤ 1
} {
w �
-3
≤w
≤ 7
} {
t �
-6
≤t
≤ 2
}
-6
-5
-4
-3
-2
-1
01
2
-
8-
6-
4-
20
24
68
-8
-6
-4
-2
02
46
8
7. �
2x
� ≤ 8
8.
� 5y
- 2
� ≤
7
9. �
p -
0.2
� <
0.5
{
x �
-4
≤ x
≤ 4
} {y
� -
1 ≤
y ≤
1 4 −
5 }
{p
� -
0.3
< p
< 0
.7}
-3
-4
-2
-1
01
23
4
-
3-
4-
2-
10
12
34
-0.
8-
0.4
00.
40.
8
If �
x � <
n,
the
n x
> -
n a
nd
x <
n.
Now
gra
ph t
he
solu
tion
set
.
-2
-1
-4
-5
-3
01
23
5-5
Exam
ple
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
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4.in
dd
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/21/
10
5:18
PM
Answers (Lesson 5-4 and Lesson 5-5)
A13_A21_ALG1_A_CRM_C05_AN_661384.indd A13A13_A21_ALG1_A_CRM_C05_AN_661384.indd A13 12/22/10 5:41 PM12/22/10 5:41 PM
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lencoe/M
cGraw
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ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
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cGraw
-Hill C
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PDF Pass
Chapter 5 A14 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
30
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Ineq
ualiti
es I
nvo
lvin
g A
bso
lute
Valu
e
Solv
e A
bso
lute
Val
ue
Ineq
ual
itie
s (>
) W
hen
sol
vin
g in
equ
alit
ies
that
in
volv
e ab
solu
te v
alu
e, t
her
e ar
e tw
o ca
ses
to c
onsi
der
for
ineq
ual
itie
s in
volv
ing
> (
or ≥
). R
emem
ber
that
in
equ
alit
ies
wit
h o
r ar
e re
late
d to
un
ion
s.
S
olve
� 2
b +
9 �
> 5
. Th
en g
rap
h t
he
solu
tion
set
.
Wri
te �
2b +
9 �
> 5
as
� 2b
+ 9
� >
5 o
r � 2b
+ 9
� <
-5.
2b +
9 >
5
or
2b +
9 <
-5
2b +
9 -
9 >
5 -
9
2b
+ 9
- 9
< -
5 -
9
2b >
-4
2b
< -
14
2b
−
2 >
-4
−
2 2b
−
2
< -
14
−
2
b >
-2
b
< -
7
Th
e so
luti
on s
et i
s {b
� b
> -
2 or
b <
-7 }
.
Exer
cise
sS
olve
eac
h i
neq
ual
ity.
Th
en g
rap
h t
he
solu
tion
set
.
1. �
c -
2 �
> 6
2.
� x
- 3
� >
0
3. �
3f +
10
� ≥
4
{
c �
c <
-4
or
c >
8}
{x
� x
> 3
or
x <
3}
{f �
f ≤
-4
2 −
3 o
r f
≥ -
2 }
20
-2
-4
-6
46
810
0-
1-
2-
3-
41
23
4
-
6-
5-
4-
3-
2-
10
12
4. �
x � ≥
2
5. �
x � ≥
3
6. �
2x +
1 � ≥
-2
{
x �
x ≤
-2
or
x ≥
2}
{x
� x
≤ -
3 o
r x ≥
3}
{x
� x
is a
rea
l num
ber}
-4
-3
-2
-1
01
23
4
0
-1
-2
-3
-4
12
34
0-
1-
2-
3-
41
23
4
7. �
2d
- 1
� ≥
4
8. �
3 -
(x
- 1
) � ≥
8
9. �
3r +
2 �
> -
5
{d
� d
≤ -
1 1 −
2 o
r d
≥ 2
1 −
2 }
{x
� x
≤ -
4 o
r x ≥
12}
{
r � r
is a
rea
l num
ber}
-4
-3
-2
-1
01
23
4
-
4-
20
24
68
1012
0-
1-
2-
3-
41
23
4
5-5
-9
-8
-7
-6
-5
-4
-3
-2
0-
1
Now
gra
ph t
he
solu
tion
set
.
Exam
ple
023_
042_
ALG
1_A
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M_C
05_C
R_6
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4.in
dd
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10
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-5
Cha
pte
r 5
31
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceIn
eq
ualiti
es I
nvo
lvin
g A
bso
lute
Valu
e
Mat
ch e
ach
op
en s
ente
nce
wit
h t
he
grap
h o
f it
s so
luti
on s
et.
1.
� x
� >
2 b
a.
-
2-
3-
4-
5-
10
12
34
5
2.
� x
- 2
� ≤
3 c
b
. -
2-
3-
4-
5-
10
12
34
5
3.
� x
+ 1
� <
4 a
c.
-
2-
3-
4-
10
12
34
56
Exp
ress
eac
h s
tate
men
t u
sin
g an
in
equ
alit
y in
volv
ing
abso
lute
val
ue.
4. T
he
wea
ther
man
pre
dict
ed t
hat
th
e te
mpe
ratu
re w
ould
be
wit
hin
3°
of 5
2°F.
� x -
52
� ≤
3
5. S
eren
a w
ill
mak
e th
e B
tea
m i
f sh
e sc
ores
wit
hin
8 p
oin
ts o
f th
e te
am a
vera
ge o
f 92
.
� x -
92
� ≤
8
6. T
he
dan
ce c
omm
itte
e ex
pect
s at
ten
dan
ce t
o n
um
ber
wit
hin
25
of l
ast
year
’s 8
7 st
ude
nts
. � x -
87
� ≤
25
Sol
ve e
ach
in
equ
alit
y. T
hen
gra
ph
th
e so
luti
on s
et.
7. �
x +
1 �
< 0
8.
� c
- 3
� <
1
9. �
n +
2 �
≥ 1
10
. � t
+ 6
� >
4
11. �
w -
2 �
< 2
12
. � k
- 5
� ≤
4
-8
-7
-10
-9
-6
-5
-4
-3
-2
-1
0-
2-
1-
4-
5-
6-
30
12
34
-3
-1
01
23
45
6-
27
-3
-4
-5
-6
-2
-1
01
23
4
5-5
-3
-4
-2
-1
01
23
45
60
12
34
56
78
910
{c �
2 <
c <
4}
{n �
n ≥
-1
or
n ≤
- 3
}{t
� t
< -
10 o
r t
> -
2}
no s
olu
tion
{w �
0 <
w <
4}
{k �
1 ≤
k ≤
9}
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
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/22/
10
5:33
PM
Answers (Lesson 5-5)
A13_A21_ALG1_A_CRM_C05_AN_661384.indd A14A13_A21_ALG1_A_CRM_C05_AN_661384.indd A14 12/22/10 5:42 PM12/22/10 5:42 PM
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pyr
ight
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oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 5 A15 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
32
Gle
ncoe
Alg
ebra
1
Prac
tice
Ineq
ualiti
es I
nvo
lvin
g A
bso
lute
Valu
e
Mat
ch e
ach
op
en s
ente
nce
wit
h t
he
grap
h o
f it
s so
luti
on s
et.
1. �
x -
3 �
≥ 1
a
a.
2. �
2x
+ 1
� <
5 c
b
.
3. �
5 -
x �
≥ 3
b
c.
Exp
ress
eac
h s
tate
men
t u
sin
g an
in
equ
alit
y in
volv
ing
abso
lute
val
ue.
4. T
he
hei
ght
of t
he
plan
t m
ust
be
wit
hin
2 i
nch
es o
f th
e st
anda
rd 1
3-in
ch s
how
siz
e.
�
h -
13
� ≤
2
5. T
he
maj
orit
y of
gra
des
in S
ean
’s E
ngl
ish
cla
ss a
re w
ith
in 4
poi
nts
of
85.
�
g -
85
� ≤
4
Sol
ve e
ach
in
equ
alit
y. T
hen
gra
ph
th
e so
luti
on s
et.
6. |
2z -
9|
≤ 1
{z
� 4
≤ z
≤ 5
} 7.
|3
- 2
r| >
7 {
r � r
< -
2 o
r r
> 5
}
8. |
3t +
6|
< 9
{t
� -
5 <
t <
1}
9. |
2g -
5|
≥ 9
{g
� g
≤ -
2 o
r g
≥ 7
}
Wri
te a
n o
pen
sen
ten
ce i
nvo
lvin
g ab
solu
te v
alu
e fo
r ea
ch g
rap
h.
10.
11.
�
x -
6 � <
5
�
x +
4 � >
2 12
. 13
.
�
x +
3 �
≥ 4
� x
- 2
� ≤
4
14. R
ESTA
UR
AN
TS T
he
men
u a
t Je
ann
e’s
favo
rite
res
tau
ran
t st
ates
th
at t
he
roas
ted
chic
ken
wit
h v
eget
able
s en
tree
typ
ical
ly c
onta
ins
480
Cal
orie
s. B
ased
on
th
e si
ze o
f th
e ch
icke
n, t
he
actu
al n
um
ber
of C
alor
ies
in t
he
entr
ee c
an v
ary
by a
s m
any
as 4
0 C
alor
ies
from
th
is a
mou
nt.
a. W
rite
an
abs
olu
te v
alu
e in
equ
alit
y to
rep
rese
nt
the
situ
atio
n.
� x -
480
� ≤
40
b.
Wh
at i
s th
e ra
nge
of
the
nu
mbe
r of
Cal
orie
s in
th
e ch
icke
n e
ntr
ee?
440
≤ x
≤ 5
20
-2
-3
-1
01
23
45
67
-2
-3
-4
-5
-6
-7
-8
-1
01
2
12
34
56
78
910
11
-2
-1
01
23
45
67
8-
5-
4-
3-
2-
10
12
34
5
-5
-4
-3
-2
-1
01
23
45
-5
-4
-3
-2
-1
01
23
45
-2
-3
-4
-5
-1
01
23
45
-2
-1
01
23
45
67
8
-2
-3
-4
-5
-1
01
23
45
5-5
-2
-3
-4
-5
-6
-7
-8
-1
01
2
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NA
ME
DAT
E
P
ER
IOD
Lesson 5-5
Cha
pte
r 5
33
Gle
ncoe
Alg
ebra
1
Wor
d Pr
oble
m P
ract
ice
Ineq
ualiti
es I
nvo
lvin
g A
bso
lute
Valu
e
1. S
PEED
OM
ETER
S T
he
gove
rnm
ent
requ
ires
spe
edom
eter
s on
car
s so
ld i
n
the
Un
ited
Sta
tes
to b
e ac
cura
te w
ith
in
±2.
5% o
f th
e ac
tual
spe
ed o
f th
e ca
r. If
yo
ur
spee
dom
eter
rea
ds 6
0 m
iles
per
h
our
wh
ile
you
are
dri
vin
g on
a h
igh
way
, w
hat
is
the
ran
ge o
f po
ssib
le a
ctu
al
spee
ds a
t w
hic
h y
our
car
cou
ld b
e tr
avel
ing?
{x|
58.5
≤x
≤ 6
1.5}
2. B
AK
ING
Pet
e is
mak
ing
mu
ffin
s fo
r a
bake
sal
e. B
efor
e h
e st
arts
bak
ing,
he
goes
on
lin
e to
res
earc
h d
iffe
ren
t m
uff
in
reci
pes.
Th
e re
cipe
s th
at h
e fi
nds
all
sp
ecif
y ba
kin
g te
mpe
ratu
res
betw
een
35
0°F
an
d 40
0°F,
in
clu
sive
. Wri
te a
n
abso
lute
val
ue i
nequ
alit
y to
rep
rese
nt t
he
poss
ible
tem
pera
ture
s t
call
ed f
or i
n t
he
mu
ffin
rec
ipes
Pet
e is
res
earc
hin
g.
|t-
375
| ≤ 2
5
3. A
RC
HER
Y I
n a
n O
lym
pic
arch
ery
even
t,
the
cen
ter
of t
he
targ
et i
s se
t ex
actl
y 13
0 ce
nti
met
ers
off
the
grou
nd.
To
get
the
hig
hes
t sc
ore
of t
en p
oin
ts, a
n a
rch
er
mu
st s
hoo
t an
arr
ow n
o fu
rth
er t
han
3.
05 c
enti
met
ers
from
th
e ex
act
cen
ter
of
the
targ
et.
a. W
rite
an
abs
olu
te v
alu
e in
equ
alit
y to
re
pres
ent
the
poss
ible
dis
tan
ces
dfr
om t
he
grou
nd
an a
rch
er c
an h
it t
he
targ
et a
nd
stil
l sc
ore
ten
poi
nts
.
|d-
130
|≤
3.0
5
b.
Gra
ph t
he
solu
tion
set
of
the
ineq
ual
ity
you
wro
te i
n p
art
a.
124
126
128
130
132
134
4. C
ATS
Du
rin
g a
rece
nt
visi
t to
th
e ve
teri
nar
ian
’s o
ffic
e, M
rs. V
an A
llen
was
in
form
ed t
hat
a h
ealt
hy
wei
ght
for
her
ca
t is
app
roxi
mat
ely
10 p
oun
ds, p
lus
or
min
us
one
pou
nd.
Wri
te a
n a
bsol
ute
va
lue
ineq
ual
ity
that
rep
rese
nts
u
nh
ealt
hy
wei
ghts
w f
or h
er c
at.
⎪ w-
10⎥
≥ 1
5. S
TATI
STIC
S T
he
mos
t fa
mil
iar
stat
isti
cal
mea
sure
is
the
arit
hm
etic
m
ean
, or
aver
age.
A s
econ
d im
port
ant
stat
isti
cal
mea
sure
is
the
stan
dard
de
viat
ion
, wh
ich
is
a m
easu
re o
f h
ow f
ar
the
indi
vidu
al s
core
s de
viat
e fr
om t
he
mea
n. F
or e
xam
ple,
in
a r
ecen
t ye
ar t
he
mea
n s
core
on
th
e m
ath
emat
ics
sect
ion
of
th
e S
AT
tes
t w
as 5
15 a
nd
the
stan
dard
de
viat
ion
was
114
. Th
is m
ean
s th
at
peop
le w
ith
in o
ne
devi
atio
n o
f th
e m
ean
h
ave
SA
T m
ath
sco
res
that
are
no
mor
e th
an 1
14 p
oin
ts h
igh
er o
r 11
4 po
ints
lo
wer
th
an t
he
mea
n.
a. W
rite
an
abs
olu
te v
alu
e in
equ
alit
y to
fin
d th
e ra
nge
of
SA
T m
ath
emat
ics
test
sco
res
wit
hin
on
e st
anda
rd
devi
atio
n o
f th
e m
ean
.
|x-
515
| ≤ 1
14
b.
Wh
at i
s th
e ra
nge
of
SA
T
mat
hem
atic
s te
st s
core
s ±
2 st
anda
rd
devi
atio
n f
rom
th
e m
ean
?
287
to 7
43
5-5
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Answers (Lesson 5-5)
A13_A21_ALG1_A_CRM_C05_AN_661384.indd A15A13_A21_ALG1_A_CRM_C05_AN_661384.indd A15 12/21/10 6:14 PM12/21/10 6:14 PM
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF 2nd
Chapter 5 A16 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
34
G
lenc
oe A
lgeb
ra 1
Enri
chm
ent
Pre
cis
ion
of
Measu
rem
en
tT
he
prec
isio
n o
f a
mea
sure
men
t de
pen
ds b
oth
on
you
r ac
cura
cy i
n
mea
suri
ng
and
the
nu
mbe
r of
div
isio
ns
on t
he
rule
r yo
u u
se. S
upp
ose
you
mea
sure
d a
len
gth
of
woo
d to
th
e n
eare
st o
ne-
eigh
th o
f an
in
ch
and
got
a le
ngt
h o
f 6
5 −
8 i
nch
es.
Th
e dr
awin
g sh
ows
that
th
e ac
tual
mea
sure
men
t li
es s
omew
her
e
betw
een
6 9 −
16
an
d 6
11
−
16 i
nch
es. T
his
mea
sure
men
t ca
n b
e w
ritt
en u
sin
g
the
sym
bol
±, w
hic
h i
s re
ad p
lus
or m
inu
s. I
t ca
n a
lso
be w
ritt
en a
s a
com
pou
nd
ineq
ual
ity.
6 5 −
8 ±
1 −
16
in
.
6
9 −
16
in
. ≤ m
≤ 6
11
−
16 i
n.
In t
his
exa
mpl
e,
1 −
16
in
ch i
s th
e ab
solu
te e
rror
. Th
e ab
solu
te e
rror
is
one-
hal
f th
e sm
alle
st u
nit
use
d in
a m
easu
rem
ent.
Wri
te e
ach
mea
sure
men
t as
a c
omp
oun
d i
neq
ual
ity.
Use
th
e va
riab
le m
.
1. 5
1 −
2 ±
1 −
4 i
n.
2. 3
.78
± 0
.005
kg
3. 7
.11
± 0
.005
g
5
1
−
4 i
n.
≤ m
≤ 5
3
−
4 i
n.
3.7
75 k
g ≤
m ≤
7
.105 g
≤ m
≤ 7
.115 g
3
.785 k
g
4. 1
6 ±
1 −
2 y
d 5.
22
± 0
.5 c
m
6.
9 −
16
±
1 −
32
in
.
1
5 1
−
2 y
d ≤
m ≤
16 1
−
2 y
d
21.
5 c
m ≤
m ≤
17
−
32 i
n.
≤ m
≤ 1
9
−
32 i
n.
2
2.5
cm
For
eac
h m
easu
rem
ent,
giv
e th
e sm
alle
st u
nit
use
d a
nd
th
e ab
solu
te e
rror
.
7. 9
.5 i
n. ≤
m ≤
10.
5 in
. 8.
4 1 −
4 i
n. ≤
m ≤
4 3 −
4 i
n.
1
in
., 0
.5 i
n.
1
−
2 i
n., 1
−
4 i
n.
9. 2
3 1 −
2 cm
≤ m
≤ 2
4 1 −
2 c
m
10. 7
.135
mm
≤ m
≤ 7
.145
mm
1
cm
, 1
−
2 c
m
0.0
1 m
m, 0.0
05 m
m
56
78
65 – 8
5-5
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-5
Cha
pte
r 5
35
G
lenc
oe A
lgeb
ra 1
Gra
phin
g Ca
lcul
ator
Act
ivit
yA
bso
lute
Valu
e I
neq
ualiti
es
Th
e T
ES
T m
enu
can
be
use
d to
sol
ve a
nd
grap
h a
bsol
ute
val
ue
ineq
ual
itie
s by
usi
ng
the
equ
ival
ent
com
pou
nd
ineq
ual
itie
s re
late
d to
abs
olu
te v
alu
e.
Exer
cise
sG
rap
h a
nd
sol
ve e
ach
in
equ
alit
y.
1. |x
+ 3
| ≥
2
2. |
2x +
6|
≤ 4
3
. ⎪ 2
- 4
x −
5
⎥ >
2
4. |
x +
8|
< -
3
G
rap
h a
nd
sol
ve e
ach
in
equ
alit
y.
a.
| x +
4|
≥ 8
En
ter
the
ineq
ual
ity
into
Y1.
Th
en e
nte
r th
e eq
uiv
alen
t co
mpo
un
d in
equ
alit
y in
to Y
2 an
d gr
aph
to
view
th
e re
sult
s. B
e su
re t
o ch
oose
ap
prop
riat
e se
ttin
gs f
or t
he
view
win
dow
.K
eyst
roke
s:
MA
TH
EN
TE
R
+ 4
)
2nd
[T
ES
T]
4 8
EN
TE
R
+ 4
2nd
[T
ES
T]
6 (–
) 8
2nd
[T
ES
T]
2
+ 4
2nd
[T
ES
T]
4 8
EN
TE
R
GR
AP
H.
Use
TR
AC
E t
o co
nfi
rm t
he
solu
tion
. Wh
en y
= 1
th
e st
atem
ent
is
tru
e, a
nd
wh
en y
= 0
th
e st
atem
ent
is f
alse
. Th
us,
th
e so
luti
on i
s x
≤
-12
or
x ≥
4.
b.
⎪ 5x +
2
−
4 ⎥
≤ 7
En
ter
the
ineq
ual
ity
into
Y1
and
the
equ
ival
ent
com
pou
nd
ineq
ual
itie
s in
to Y
2. T
hen
gra
ph t
he
solu
tion
set
.K
eyst
roke
s:
MA
TH
EN
TE
R
( 5
+
2
)
÷ 4
)
2nd
[T
ES
T]
6 7
EN
TE
R
( 5
+
2
)
÷ 4
2nd
[TE
ST
] 4
(–) 7
2nd
[T
ES
T]
EN
TE
R
( 5
+
2
)
÷
4
2nd
[T
ES
T]
6 7
EN
TE
R
GR
AP
H.
Th
e st
atem
ent
is t
rue
betw
een
-6
and
5.2.
Th
us
the
solu
tion
is
-
6 ≤
x ≤
5.2
.
[-18.8
, 18.8
] scl:
2 b
y [
-3.1
, 3.1
] scl:
1
[-18.8
, 18.8
] scl:
2 b
y [
-3.1
, 3.1
] scl:
1
[-18.8
, 18.8
] scl:
2 b
y [
-3.1
, 3.1
] scl:
1
[-18.8
, 18.8
] scl:
2 b
y [
-3.1
, 3.1
] scl:
1
5-5 x
≤
-5
or
x ≥
-1
-5
≤ x
≤ -
1x
<
-2
or
x >
3
Exam
ple
no
so
luti
on
023_
042_
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Answers (Lesson 5-5)
A13_A21_ALG1_A_CRM_C05_AN_661384.indd A16A13_A21_ALG1_A_CRM_C05_AN_661384.indd A16 12/24/10 7:59 AM12/24/10 7:59 AM
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pyr
ight
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lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 5 A17 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
36
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
Gra
ph
ing
In
eq
ualiti
es i
n T
wo
Vari
ab
les
Gra
ph
Lin
ear
Ineq
ual
itie
s T
he
solu
tion
set
of
an i
neq
ual
ity
that
in
volv
es t
wo
vari
able
s is
gra
phed
by
grap
hin
g a
rela
ted
lin
ear
equ
atio
n t
hat
for
ms
a bo
un
dary
of
a h
alf-
pla
ne.
Th
e gr
aph
of
the
orde
red
pair
s th
at m
ake
up
the
solu
tion
set
of
the
ineq
ual
ity
fill
a r
egio
n o
f th
e co
ordi
nat
e pl
ane
on o
ne
side
of
the
hal
f-pl
ane.
G
rap
h y
≤ -
3x -
2.
Gra
ph y
= -
3x -
2.
Sin
ce y
≤ -
3x -
2 i
s th
e sa
me
as y
< -
3x -
2 a
nd
y =
-3x
- 2
, th
e bo
un
dary
is
incl
ude
d in
th
e so
luti
on s
et a
nd
the
grap
h s
hou
ld b
e dr
awn
as
a so
lid
lin
e.S
elec
t a
poin
t in
eac
h h
alf
plan
e an
d te
st i
t. C
hoo
se (
0, 0
) an
d (-
2, -
2).
y ≤
-3x
- 2
y
≤ -
3x -
2 0
≤ -
3(0)
- 2
-
2 ≤
-3(
-2)
- 2
0 ≤
-2
is f
alse
. -
2 ≤
6 -
2-
2 ≤
4 i
s tr
ue.
Th
e h
alf-
plan
e th
at c
onta
ins
(-2,
-2)
con
tain
s th
e so
luti
on. S
had
e th
at h
alf-
plan
e.
Exer
cise
sG
rap
h e
ach
in
equ
alit
y.
1. y
< 4
2.
x ≥
1
3. 3
x ≤
y
4. -
x >
y
5. x
- y
≥ 1
6.
2x
- 3
y ≤
6
7. y
< -
1 −
2 x
- 3
8.
4x
- 3
y <
6
9. 3
x +
6y
≥ 1
2
x
y
O
x
y
O
x
y
O
x
y
Ox
y
O
x
y O
x
y
Ox
y
O
x
y
O
5-6
x
y
O
Exam
ple
023_
042_
ALG
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M_C
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dd
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10
4:38
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-6
Cha
pte
r 5
37
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Gra
ph
ing
In
eq
ualiti
es i
n T
wo
Vari
ab
les
Solv
e Li
nea
r In
equ
alit
ies
We
can
use
a c
oord
inat
e pl
ane
to s
olve
in
equ
alit
ies
wit
h
one
vari
able
.
U
se a
gra
ph
to
solv
e 2x
+ 2
> -
1 .
Ste
p 1
F
irst
gra
ph t
he
bou
nda
ry, w
hic
h i
s th
e re
late
d fu
nct
ion
. R
epla
ce t
he
ineq
ual
ity
sign
wit
h a
n e
qual
s si
gn, a
nd
get
0 on
a s
ide
by i
tsel
f.
2x
+ 2
> -
1 O
rigin
al in
equalit
y
2x
+ 2
= -
1 C
hange <
to =
.
2x
+ 2
+ 1
= -
1 +
1
Add 1
to e
ach s
ide.
2x +
3 =
0
Sim
plif
y.
G
raph
2x
+ 3
= y
as
a da
shed
lin
e.
Ste
p 2
C
hoo
se (
0, 0
) as
a t
est
poin
t, s
ubs
titu
tin
g th
ese
valu
es
into
th
e or
igin
al i
neq
ual
ity
give
us
3 >
-5.
Ste
p 3
B
ecau
se t
his
sta
tem
ent
is t
rue,
sh
ade
the
hal
f pl
ane
con
tain
ing
the
poin
t (0
, 0).
Not
ice
that
th
e x-
inte
rcep
t of
th
e gr
aph
is
at -
1 1 −
2 .
Bec
ause
th
e h
alf-
plan
e to
th
e ri
ght
of t
he
x-in
terc
ept
is s
had
ed, t
he
solu
tion
is
x >
-1
1 −
2 .
Exer
cise
sU
se a
gra
ph
to
solv
e ea
ch i
neq
ual
ity.
1. x
+ 7
≤ 5
x ≤
-2
2. x
- 2
> 2
x >
4
3. -
x +
1 <
-3
x >
4
4. -
x -
7 ≥
-6
x ≤
-1
5. 3
x -
20
< -
17 x
< 1
6.
-2x
+ 1
1 ≥
15
x ≤
-2
5-6
y
x
y
x
y
xO
y
x
y
x
y
x
y
x
Exam
ple
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
3712
/21/
10
4:38
PM
Answers (Lesson 5-6)
A13_A21_ALG1_A_CRM_C05_AN_661384.indd A17A13_A21_ALG1_A_CRM_C05_AN_661384.indd A17 12/21/10 6:14 PM12/21/10 6:14 PM
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ht © G
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-Hill, a d
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cGraw
-Hill C
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ht © G
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-Hill, a d
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Chapter 5 A18 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
38
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceG
rap
hin
g I
neq
ualiti
es i
n T
wo
Vari
ab
les
Mat
ch e
ach
in
equ
alit
y to
th
e gr
aph
of
its
solu
tion
.
1. y
- 2
x <
2 b
a.
b
.
2. y
≤ -
3x d
3. 2
y -
x ≥
4 a
4. x
+ y
> 1
c
c.
d
.
Gra
ph
eac
h i
neq
ual
ity.
5. y
< -
1 6.
y ≥
x -
5
7. y
> 3
x
8. y
≤ 2
x +
4
9. y
+ x
> 3
10
. y -
x ≥
1
Use
a g
rap
h t
o so
lve
each
in
equ
alit
y.
11. 1
> 2
x +
5
12. 7
≤ 3
x +
4
13. -
1 −
2 <
- 1 −
2 x
+ 1x
y
Ox
y
Ox
y
O
x
y
O
x
y
O
x
y
O
x
y
Ox
y
O
x
y O
x
y
O
5-6 x <
-2
x ≥
1
x <
3
x
y
O
y
xO
y
x
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
3812
/21/
10
4:38
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-6
Cha
pte
r 5
39
Gle
ncoe
Alg
ebra
1
Prac
tice
Gra
ph
ing
In
eq
ualiti
es i
n T
wo
Vari
ab
les
Det
erm
ine
wh
ich
ord
ered
pai
rs a
re p
art
of t
he
solu
tion
set
for
eac
h i
neq
ual
ity.
1. 3
x +
y ≥
6, {
(4, 3
), (-
2, 4
), (-
5, -
3), (
3, -
3)}
{(4,
3),
(3, -
3)}
2. y
≥ x
+ 3
, {(6
, 3),
(-3,
2),
(3, -
2), (
4, 3
)} {
(-3,
2)}
3. 3
x -
2y
< 5
, {(4
, -4)
, (3,
5),
(5, 2
), (-
3, 4
)} {
(3, 5
), (-
3, 4
)}
Gra
ph
eac
h i
neq
ual
ity.
4. 2
y -
x <
-4
5. 2
x -
2y
≥ 8
6.
3y
> 2
x -
3
Use
a g
rap
h t
o so
lve
each
in
equ
alit
y.
7. -
5 ≤
x -
9
8. 6
> 2 −
3 x
+ 5
9.
1 −
2 >
-2
x +
7 −
2
10. M
OV
ING
A m
ovin
g va
n h
as a
n i
nte
rior
hei
ght
of 7
fee
t (8
4 in
ches
). Yo
u h
ave
boxe
s in
12
in
ch a
nd
15 i
nch
hei
ghts
, an
d w
ant
to s
tack
th
em a
s h
igh
as
poss
ible
to
fit.
Wri
te a
n
ineq
ual
ity
that
rep
rese
nts
th
is s
itu
atio
n.
12x +
15y
≤ 8
4
11. B
UD
GET
ING
Sat
chi
fou
nd
a u
sed
book
stor
e th
at s
ells
pre
-ow
ned
DV
Ds
and
CD
s. D
VD
s co
st $
9 ea
ch, a
nd
CD
s co
st $
7 ea
ch. S
atch
i ca
n s
pen
d n
o m
ore
than
$35
.
a. W
rite
an
in
equ
alit
y th
at r
epre
sen
ts t
his
sit
uat
ion
. 9x
+ 7
y ≤
35
b.
Doe
s S
atch
i h
ave
enou
gh m
oney
to
buy
2 D
VD
s an
d 3
CD
s?
No
, th
e p
urc
has
es w
ill b
e $3
9, w
hic
h is
gre
ater
th
an $
35.
x
y
O
x
y
O
x
y
O
5-6
x
y
O
x
y
O
x <
1 1 −
2
x ≥
4x >
1 1 −
2 y
x
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
3912
/21/
10
4:38
PM
Answers (Lesson 5-6)
A13_A21_ALG1_A_CRM_C05_AN_661384.indd A18A13_A21_ALG1_A_CRM_C05_AN_661384.indd A18 12/21/10 6:14 PM12/21/10 6:14 PM
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pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF 2nd
Chapter 5 A19 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
40
Gle
ncoe
Alg
ebra
1
1. F
AM
ILY
Tyr
one
said
th
at t
he
ages
of
his
si
blin
gs a
re a
ll p
art
of t
he
solu
tion
set
of
y >
2x,
wh
ere
x is
th
e ag
e of
a s
ibli
ng
and
y is
Tyr
one’
s ag
e. W
hic
h o
f th
e fo
llow
ing
ages
is
poss
ible
for
Tyr
one
and
a si
blin
g?T
yron
e is
23;
Max
ine
is 1
4.
no
Tyr
one
is 1
8; C
amil
le i
s 8.
ye
sT
yron
e is
12;
Fra
nci
s is
4.
yes
Tyr
one
is 1
1; M
arti
n i
s 6.
n
oT
yron
e is
19;
Pau
l is
9.
yes
2. F
AR
MIN
G T
he
aver
age
valu
e of
U.S
. fa
rm c
ropl
and
has
ste
adil
y in
crea
sed
in
rece
nt
year
s. I
n 2
000,
th
e av
erag
e va
lue
was
$14
90 p
er a
cre.
Sin
ce t
hen
, th
e va
lue
has
in
crea
sed
at l
east
an
ave
rage
of
$77
per
acre
per
yea
r. W
rite
an
in
equ
alit
y to
sh
ow l
and
valu
es a
bove
th
e av
erag
e fo
r fa
rmla
nd.
3. S
HIP
PIN
G A
n i
nte
rnat
ion
al s
hip
pin
g co
mpa
ny
has
est
abli
shed
siz
e li
mit
s fo
r pa
ckag
es w
ith
all
th
eir
serv
ices
. Th
e to
tal
of t
he
len
gth
of
the
lon
gest
sid
e an
d th
e gi
rth
(di
stan
ce c
ompl
etel
y ar
oun
d th
e pa
ckag
e at
its
wid
est
poin
t pe
rpen
dicu
lar
to t
he
len
gth
) m
ust
be
less
th
an o
r eq
ual
to
419
cen
tim
eter
s. W
rite
an
d gr
aph
an
in
equ
alit
y th
at r
epre
sen
ts t
his
sit
uat
ion
.
4. F
UN
DR
AIS
ING
Tro
op 2
00 s
old
cide
r an
d do
nu
ts t
o ra
ise
mon
ey f
or c
har
ity.
Th
ey
sold
sm
all
boxe
s of
don
ut
hol
es f
or $
1.25
an
d ci
der
for
$2.5
0 a
gall
on. I
n o
rder
to
cove
r th
eir
expe
nse
s, t
hey
nee
ded
to
rais
e at
lea
st $
100.
Wri
te a
nd
grap
h a
n
ineq
ual
ity
that
rep
rese
nts
th
is s
itu
atio
n.
1.25
d +
2.5
c ≥
10
0
5.IN
CO
ME
In 2
006
the
med
ian
yea
rly
fam
ily
inco
me
was
abo
ut
$48,
200
per
year
. Su
ppos
e th
e av
erag
e an
nu
al r
ate
of c
han
ge s
ince
th
en i
s $1
240
per
year
.
a. W
rite
an
d gr
aph
an
in
equ
alit
y fo
r th
e an
nu
al f
amil
y in
com
es y
th
at
are
less
th
an t
he
med
ian
for
x y
ears
af
ter
2006
.
y <
124
0x +
48,
200
b.
Det
erm
ine
wh
eth
er e
ach
of
the
foll
owin
g po
ints
is
part
of
the
solu
tion
set
. (2
, 51,
000)
n
o
(8, 6
9,20
0)
no
(5, 5
0,00
0)
yes
(10,
61,
000)
n
oO
Girth
Len
gth
100
150 50200
250
300
350
400
450
500
g
150
100
5025
035
020
030
040
0450 50
0�
Cider (gal)
Do
nu
t h
ole
s
2030 10405060708090c
3020
1050
7040
60d
O
1.25
d +
2.5
0c ≥
100
O
Income ($1000)
Year
s si
nce
200
6
46,0
00
48,0
00
44,0
00
50,0
00
52,0
00
54,0
00
56,0
00
58,0
00
y
32
15
78
910
46
x
lengt
h
girth
l + g
≤ 4
19
5-6
Wor
d Pr
oble
m P
ract
ice
Gra
ph
ing
In
eq
ualiti
es i
n T
wo
Vari
ab
les
y >
77x
+ 1
490
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
4012
/21/
10
4:38
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 5-6
Cha
pte
r 5
41
Gle
ncoe
Alg
ebra
1
Enri
chm
ent
Lin
ear
Pro
gra
mm
ing
Lin
ear
prog
ram
min
g ca
n b
e u
sed
to m
axim
ize
or m
inim
ize
cost
s. I
t in
volv
es g
raph
ing
a se
t of
lin
ear
ineq
ual
itie
s an
d u
sin
g th
e re
gion
of
inte
rsec
tion
. You
wil
l u
se l
inea
r pr
ogra
mm
ing
to s
olve
th
e fo
llow
ing
prob
lem
.
L
ayn
e’s
Gif
t S
hop
pe
sell
s at
mos
t 50
0 it
ems
per
wee
k. T
o m
eet
her
cu
stom
ers’
dem
and
s, s
he
sell
s at
lea
st 1
00 s
tuff
ed a
nim
als
and
75
gree
tin
g ca
rds.
If
th
e p
rofi
t fo
r ea
ch s
tuff
ed a
nim
al i
s $2
.50
and
th
e p
rofi
t fo
r ea
ch g
reet
ing
card
is
$1.
00, t
he
equ
atio
n P
(a, g
) =
2.5
0a +
1.0
0g c
an b
e u
sed
to
rep
rese
nt
the
pro
fit.
H
ow m
any
of e
ach
sh
ould
sh
e se
ll t
o m
axim
ize
her
pro
fit?
Wri
te t
he
ineq
ual
itie
s:
G
raph
th
e in
equ
alit
ies:
a +
g ≤
500
a ≥
100
g ≥
75
Fin
d th
e ve
rtic
es o
f th
e tr
ian
gle
form
ed: (
100,
75)
, (10
0, 4
00),
and
(425
, 75)
Su
bsti
tute
th
e va
lues
of
the
vert
ices
in
to t
he
equ
atio
n f
oun
d ab
ove:
2.
50(1
00)
+ 1
(75)
= 3
25
2.
50(1
00)
+ 1
(400
) =
650
2.50
(425
) +
1(7
5) =
113
7.50
T
he
max
imu
m p
rofi
t is
$11
37.5
0.
Exer
cise
s T
he
Sp
irit
Clu
b i
s se
llin
g sh
irts
an
d b
ann
ers.
Th
ey s
ell
at m
ost
400
of t
he
two
item
s. T
o m
eet
the
dem
and
s of
th
e st
ud
ents
, th
ey m
ust
sel
l at
lea
st 5
0 T-
shir
ts a
nd
10
0 b
ann
ers.
Th
e p
rofi
t on
eac
h s
hir
t is
$4.
00 a
nd
th
e p
rofi
t on
eac
h b
ann
er i
s $1
.50,
th
e eq
uat
ion
P(t
, b)
= 4
.00t
+ 1
.50b
can
be
use
d t
o re
pre
sen
t th
e p
rofi
t. H
ow
man
y sh
ould
th
ey s
ell
of e
ach
to
max
imiz
e th
e p
rofi
t?
1. W
rite
th
e in
equ
alit
ies
to r
epre
sen
t th
is s
itu
atio
n.
t +
b ≤
40
0; t
≥ 5
0; b
≥ 1
00
2. G
raph
th
e in
equ
alit
ies
from
Exe
rcis
e 1.
See
gra
ph
at
rig
ht.
3. F
ind
the
vert
ices
of
the
figu
re f
orm
ed.
(50,
10
0), (
50, 3
50),
(30
0, 1
00)
4. W
hat
is
the
max
imu
m p
rofi
t th
e S
piri
t C
lub
can
mak
e?
$135
0
b
tO
100
300
400
500
100
200
200
300
400
500
g
aO
100
-30
0
-40
0
-50
0
-10
0
-20
0
200
300
400
500
5-6
Exam
ple
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
4112
/24/
10
11:3
5 A
M
Answers (Lesson 5-6)
A13_A21_ALG1_A_CRM_C05_AN_661384.indd A19A13_A21_ALG1_A_CRM_C05_AN_661384.indd A19 12/24/10 11:38 AM12/24/10 11:38 AM
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 5 A20 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 5
42
Gle
ncoe
Alg
ebra
1
Spre
adsh
eet
Act
ivit
yIn
eq
ualiti
es i
n T
wo
Vari
ab
les
You
can
use
a s
prea
dsh
eet
to d
eter
min
e w
het
her
ord
ered
pai
rs s
atis
fy a
n i
neq
ual
ity.
Exer
cise
sU
se a
sp
read
shee
t to
det
erm
ine
wh
ich
ord
ered
pai
rs a
re p
art
of t
he
solu
tion
set
for
eac
h i
neq
ual
ity.
1. 2
x +
3y
> 1
; {(0
, 3),
(1, -
3), (
-2,
-1)
, (6,
8)}
{(0
, 3),
(6, 8
)}
2. 7
x -
y <
8; {
(1, 2
), (-
3, -
1), (
0, -
10),
(6, 9
)} {
(1, 2
), (-
3, -
1)}
3. y
≥ 3
x; {
(3, 1
), (-
4, 5
), (-
1, 0
), (7
, -1)
, (2,
7)}
{(-
4, 5
), (-
1, 0
), (2
, 7)}
4. y
≤ -
4x; {
(9, 3
), (-
3, 5
), (0
, 0),
(12,
1),
(3, 9
)} {
(-3,
5),
(0, 0
)}
5. y
> 1
2 -
2x;
{(-
3, -
3), (
-1,
9),
(12,
13)
, (-
4, 1
1)}
{(12
, 13)
}
6. y
> 2
+ 6
x; {
(0, -
4), (
-4,
8),
(9, 1
7), (
-2,
18)
, (-
5, -
5)}
{(-
4, 8
), (-
2, 1
8), (
-5,
-5)
}
7. |
x +
1|
≤ y
; {(1
, -8)
, (0,
4),
(5, 1
6), (
-2,
-8)
, (11
, -2)
} {(
0, 4
), (5
, 16)
}
8. |
y -
7|
< x
; {(5
, 8),
(-1,
3),
(2, 1
9), (
-6,
-6)
, (10
, -22
)} {
(5, 8
)}
U
se a
sp
read
shee
t to
det
erm
ine
wh
ich
ord
ered
pai
rs f
rom
th
e se
t {(
2, 3
), (
4, 1
), (
-1,
2),
(0,
7),
(-
8, -
10)}
are
par
t of
th
e so
luti
on s
et f
or 5
x -
2y
> 1
2.
Ste
p 1
U
se c
olu
mn
s A
an
d B
of
the
spre
adsh
eet
for
the
repl
acem
ent
set.
E
nte
r th
e x-
coor
din
ates
in
col
um
n A
an
d th
e y-
coor
din
ates
in
col
um
n B
.
Ste
p 2
C
olu
mn
C c
onta
ins
the
form
ula
for
th
e in
equ
alit
y.
Use
th
e n
ames
of
the
cell
s co
nta
inin
g th
e x-
an
d y-
coor
din
ates
of
each
ord
ered
pai
r to
det
erm
ine
wh
eth
er t
hat
ord
ered
pai
r is
par
t of
th
e so
luti
on
set.
Th
e fo
rmu
la w
ill
retu
rn T
RU
E o
r F
AL
SE
.
Th
e so
luti
on s
et c
onta
ins
the
orde
red
pair
s fo
r w
hic
h t
he
ineq
ual
ity
is t
rue.
Th
e or
dere
d pa
ir {
(4, 1
)} i
s pa
rt o
f th
e so
luti
on s
et o
f 5x
- 2
y >
12.
Th
e sp
read
shee
t ca
n a
lso
eval
uat
e in
equ
alit
ies
invo
lvin
g ab
solu
te v
alu
e. E
nte
r an
abs
olu
te v
alu
e ex
pres
sion
lik
e |x
| u
sin
g th
e fu
nct
ion
AB
S(x
).
A1 4 5 6 72 3
BC
y5x
- 2
y >
12=
5*A
2-2
*B2>
12
=5*A
3-2
*B3>
12
=5*A
4-2
*B4>
12
=5*A
5-2
*B5>
12
=5*A
6-2
*B6>
12
x2 4 -1 0 -8
3 1 2 7
-10
Sh
eet
1S
hee
t 2
Sh
eet
3
A1 4 5 6 72 3
BC
y5x
- 2
y >
12x
2 4 -1 0 -8
3 1 2 7
-10
FA
LS
E
TR
UE
FA
LS
E
FA
LS
E
FA
LS
E
Sh
eet
1S
hee
t 2
Sh
eet
3
5-6
Exam
ple
023_
042_
ALG
1_A
_CR
M_C
05_C
R_6
6138
4.in
dd
4212
/21/
10
4:38
PM
Answers (Lesson 5-6)
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-Hill C
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PDF 2nd
Chapter 5 A22 Glencoe Algebra 1
{w | w ≤ -14}
1.
-15-16-17-18 -14-13 -11-10-12
2.
3.
4.
5.
{n � n ≥ -28}
Sample answer: n = the number;
n - 7 ≥ 15; {n � n ≥ 22}
{m � m > -78}
B
1.
2.
3.
4.
5.
Ø
{d � d ≤ -100}
Sample answer: n = the number; n + 3 < 19 - n;
{ n |n < 8 }
D
{t � t > 6}
1.
2.
3.
4.
5.
B
1.
2.
3.
4.
5.
D
{x � 0 < x ≤ 3}
� x � > 1
{x � -1 ≤ x ≤ 3}
{x � x ≥ 2 or ≤ -1}
yes
-4 54321-3 0-1-2
-4 54321-3 0-1-2
-4 54321-3 0-1-2
y
xO x < 3
y
xO
-2(x -y )≤ 4
y
xO
x +1 ≤ y13
Chapter 5 Assessment Answer KeyQuiz 1 (Lessons 5-1 and 5-2) Quiz 3 (Lessons 5-4 and 5-5) Mid-Chapter TestPage 45 Page 46 Page 47
Quiz 2 (Lessons 5-3)
Page 45
1.
2.
3.
4.
5.
6.
7.
8.
9.
Sample answer:
a = no. of apples;
6a ≥ 50; at least 8 1 − 3
apples
Sample answer:
� = length; � + 63 ≤ 85;
22 in. or less
C
J
B
F
{t | t < 15.2}
{x | x > 4}
C
1 1098762 543
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PDF Pass
Chapter 5 A23 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
intersection
half-plane
compound inequality
boundary
union
Sample answer: An open
half-plane is the half of a
coordinate grid that
contains all solutions to
an inequality, boundary
included.
Sample answer: Set-
builder notation is a way
of writing a solution set.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. J
C
F
C
G
D
J
A
J
B
H
A
13.
14.
15.
16.
17.
18.
19.
20. G
A
G
B
J
A
G
A
-1B:
Chapter 5 Assessment Answer KeyVocabulary Test Form 1Page 48 Page 49 Page 50
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Chapter 5 Assessment Answer KeyForm 2A Form 2BPage 51 Page 52 Page 53 Page 54
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. C
F
D
H
D
G
A
J
A
F
C
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-Hill C
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PDF Pass
Chapter 5 A24 Glencoe Algebra 1
12.
13.
14.
15.
16.
17.
18.
19.
20. G
B
J
D
J
G
A
A
H
{n � -12 ≤ n ≤ 12}B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. C
F
D
H
B
H
A
J
D
F
A 12.
13.
14.
15.
16.
17.
18.
19.
20. F
A
J
J
A
H
B
C
H
{x |-3 ≤ x < 4}B:
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Chapter 5 Assessment Answer KeyForm 2CPage 55 Page 56
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Chapter 5 A25 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
-1-2-3-4 0 1 2 43
-1-2-3-4 0 1 2 43
{x |x ≤ 1 or x ≥ 2}
-1-2-3-4 0 1 2 43
0-1-2-3-4 1 2 43
-1-2-3-4-5-6 0 1 2
{x |x > 13}
131211109 14 15 1716
{x |x < 3}
{c |c ≤ 13}
{x |x is a real number}
{w |-5 < w < 2}
{p |p ≤ 2}
{x |x < 8}
{r |r > -5.5}
{y |y ≤ -5.5}
{t |t ≥ 84}
{
b|b > -1 3 −
5 }
{z |z < -4}
{x | -1 ≤ x ≤ 3}
15.
16.
17.
18.
19.
20.
B:
3x + 0.75y ≤ 20; No, the cost
would be more than $20.00.
y < x - 1
y
xO
y = - x + 2 13
y
xO
2x - 3y ≤ 6
Sample answer:
x = car price;
� 6000 - x �
≤
1500;
{x � 4500 ≤ x ≤ 7500}; from
$4500 to $7500
{x | -2 < x < 1.5}
-3 1 117
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Chapter 5 Assessment Answer KeyForm 2DPage 57 Page 58
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Chapter 5 A26 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
{w| -3 ≤ w ≤ 5}-11 30
-1-2-3-4 0 1 2 43
0-1-2-3-4 1 2 3 4
-1-2-3-4 0 1 2 43
1312111098 14 15 16
{x | x > -11}
{x | x > 2}
{w | w is a real number}
{w | 2 < w < 3}
{w | w > -5}
{t | t ≤ -5.5}
{m | m > 6}
{k | k ≤ 3.5}
{
z | z < -3 1 −
3 }
{h | h < 27}
{k|k ≥ 5}
{y |y ≤ 12}
{z | z ≤ -11 or z ≥ 3}
{x| 1 < x < 4}-1-2-3 0 1 2 4 53
16.
17.
18.
19.
20.
B:
28x + 4y ≤ 75;
no, the cost would be more than $75.00.
Sample answer: x = boat
price; � 4500 - x � ≤ 1300; {x � 3200 ≤ x ≤ 5800}; from
$3200 to $5800
y
xO
y = 3x
2x - y ≤ 1
y
xO
2y - 4x < 8
-7 -5 3 5
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Chapter 5 Assessment Answer KeyForm 3Page 59 Page 60
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Chapter 5 A27 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
9.3
3635343332 37 38 4039
Sample answer: s = amount of sales; 32,500 < 0.1s + 25,600 < 41,900; between $69,000 and $163,000
Sample answer: n = small positive even integer; n + n + 2 ≤ 15; 6, 8; 4, 6; 2, 4
Sample answer: j = cost of jeans;
2(19.89) + j ≤ 78; no more than $38.22
Ø
{x | x ≤ -9}
{b | b < 0.5}
{t | t >
9 −
11 }
{w | w ≤ -10.4}
Sample answer: n = the
number; n - 15 > 2n + 8;
{n | n < -23}
Sample answer: n = the number;
{t | t < 36}
{m |m ≥ 9.3}
-
3
−
7 + n ≥ 2; {n | n ≥ 2 3
−
7 }
13.
14.
-6 80
15.
16.
17.
18.
19.
20.
B:
-1-2-3-4-5-6-7-8-9
-1-2 0 1 2 4 5 63
-1-2 0 1 2 4 5 63
y
xO
x + 3y > -12
y
xO
-y = 3x
16x + 12y ≤ 120; 3
{x|x ≤ -1 or x ≥ 4}
{x |-2 < x < 6}
{x |-6 < x ≤ 8}
{n|n > -6}
False; sample answer: x > 3 and y > 1. If xy < 0, x and y cannot both be positive, so x > 3 and y > 1 is false.
{x|x ≤ -2.8 or x ≥ 4}
-2.8 40
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Chapter 5 Assessment Answer Key Page 61, Extended-Response Test Scoring Rubric
Score General Description Specifi c Criteria
4 Superior
A correct solution that
is supported by well-
developed, accurate
explanations
• Shows thorough understanding of the concepts of using the properties of inequalities, solving inequalities, solving compound inequalities, solving open sentences involving absolute value, and graphing inequalities in two variables.
• Uses appropriate strategies to solve problems.
• Computations are correct.
• Written explanations are exemplary.
• Graphs are accurate and appropriate.
• Goes beyond requirements of some or all problems.
3 Satisfactory
A generally correct solution,
but may contain minor fl aws
in reasoning or computation
• Shows an understanding of the concepts of using the properties of inequalities, solving inequalities, solving compound inequalities, solving open sentences involving absolute value, and graphing inequalities in two variables.
• Uses appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are effective.
• Graphs are mostly accurate and appropriate.
• Satisfi es all requirements of problems.
2 Nearly Satisfactory
A partially correct
interpretation and/or
solution to the problem
• Shows an understanding of most of the concepts of using the properties of inequalities, solving inequalities, solving compound inequalities, solving open sentences involving absolute value, and graphing inequalities in two variables.
• May not use appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are satisfactory.
• Graphs are mostly accurate.
• Satisfi es the requirements of most of the problems.
1 Nearly Unsatisfactory
A correct solution with no
supporting evidence or
explanation
• Final computation is correct.
• No written explanations or work is shown to substantiate the
fi nal computation.
• Graphs may be accurate but lack detail or explanation.
• Satisfi es minimal requirements of some of the problems.
0 Unsatisfactory
An incorrect solution
indicating no mathematical
understanding of the
concept or task, or no
solution is given
• Shows little or no understanding of most of the concepts of
using the properties of inequalities, solving inequalities, solving compound inequalities, solving open sentences involving absolute value, and graphing inequalities in two variables.
• Does not use appropriate strategies to solve problems.
• Computations are incorrect.
• Written explanations are unsatisfactory.
• Graphs are inaccurate or inappropriate.
• Does not satisfy requirements of problems.
• No answer may be given.
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Chapter 5 A28 Glencoe Algebra 1
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Chapter 5 Assessment Answer Key Page 61, Extended-Response Test Sample AnswersIn addition to the scoring rubric found on page A34, the following sample answers may be used as guidance in evaluating extended-response assessment items.
2a. After drawing a graph, students should write an inequality that corresponds with the line they have drawn. The inequality may or may not include equality.
2b. The solution set includes the boundary (line) if the inequality written for part a includes equality. If the inequality written for part a does not include equality, then the student should state that the solution set of the inequality does not include the line.
3. The inequality ab > 2a can be determined to be true or false by considering the value of a. Since b > 2, by the Multiplication Property of Inequality ab > 2a is true if a is a positive number.
4. The solution set for � x - 2 � > 4 is {x � x < -2 or x > 6} . The solution set for -2x < 4 or x > 6 is {x � x > -2} . One includes numbers greater than -2, and the other includes numbers less than -2 or greater than 6. These solution sets are not the same.
5a. w ≤ 90 - 2(20); {w � w ≤ 50}
5b. The formula for the area of a rectangle with 50 substituted for the width can be used to write the compound inequality 2800≤ 50 � ≤ 3200. The possible lengths are found by solving this compound inequality for �. The solution set is {� � 56 ≤ � ≤ 64} .
5c. � 175,000 - x � ≤ 20,000; 155,000 ≤ x ≤ 195,000; The Fraziers are willing to pay from $155,000 to $195,000 for the house.
1. 10n - 7(n + 2) > 5n - 12 Original inequality
10n - 7n - 14 > 5n - 12 Distributive Property
3n - 14 > 5n - 12 Combine like terms.
3n - 14 - 5n > 5n - 12 - 5n Subtract 5n from each side.
-2n - 14 > -12 Simplify.
-2n - 14 + 14 > -12 + 14 Add 14 to each side.
-2n > 2 Simplify.
-2n −
-2 < 2 ÷ (-2) Divide each side by -2. Change > to <.
n < - 1 Simplify.
The solution set is {n�n < -1} .
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Chapter 5 A29 Glencoe Algebra 1
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Chapter 5 Assessment Answer KeyStandardized Test PracticePage 62 Page 63
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. F G H J
F G H J
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
A B C D
A B C D
18.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
1 19.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
5
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Chapter 5 A30 Glencoe Algebra 1
11.
12.
13.
14.
15.
16.
17. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
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Chapter 5 Assessment Answer KeyStandardized Test PracticePage 64
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Chapter 5 A31 Glencoe Algebra 1
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30a.
30b.
21
102
y
xO
y = x - 4
a ≤ -15
y = 4x - 4
{(-4, -2), (-2, -1.5),
(0, -1), (2, -0.5), (4, 0)}
{
f |
|
-3 ≤ f ≤
5 −
3 }
$400 ≤ x ≤ $800
$428 ≤ x ≤ $856
x = 10
{a � -2 ≤ a < 5}
-4 -3 -2 -1 0 1 2 3 4
-3 -2 -1 0 1 2 3 4 5
y
xO
A22_A34_ALG1_A_CRM_C05_AN_661384.indd A31A22_A34_ALG1_A_CRM_C05_AN_661384.indd A31 12/22/10 8:02 PM12/22/10 8:02 PM