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Lesson 1-1: Expressions and Formulas Date:

are letters used to represent unknown quantities.

Expressions that contain at least one variable are called .

A is a mathematical sentence that expresses the relationship between certain

quantities.

Example 1: Evaluate Algebraic Expressions

Evaluate (𝑥 − 𝑦)3 + 3 if 𝑥 = and 𝑦 = .

Example 2: Evaluate Algebraic Expressions

Evaluate 8𝑥𝑦+𝑧3

𝑦2+5 if 𝑥 = , 𝑦 = , and 𝑧 = .

Real-World Example 3: Use a Formula

GEOMETRY The formula for the area 𝐴 of a trapezoid is 𝐴 =1

2ℎ(𝑏1 + 𝑏2), where ℎ represents the

height, and 𝑏1 and 𝑏2 represent the measures of the bases. Find the area of a trapezoid with base lengths of

13 meters and 25 meters and a height of 8 meters.

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Lesson 1-2: Properties of Real Numbers Date:

Example 1: Classify numbers

Name the sets of numbers to which each number belongs.

A. B.

C. D.

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Example 2: Name Properties of Real Numbers

Name the property illustrated by each.

A. B.

Example 3: Additive and Multiplicative Inverses

Find the additive inverse and multiplicative inverse for –7.

Example 4: Distributive Property

POSTAGE Audrey went to a post office and bought eight 42¢ stamps and eight 27¢ postcard stamps.

What was the total amount of money Audrey spent on stamps?

Example 5: Simplify an Expression

Simplify

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Lesson 1-3: Solving Equations Date:

A mathematical sentence containing one or more variables is called an .

A mathematical sentence stating that two mathematical expressions are equal is called an .

Open sentences are neither true nor false until variables have been replaced by numbers. Each

replacement that results in a true sentence is called a of the open sentence.

Example 1: Verbal to Algebraic Expression

Write an algebraic expression to represent each verbal expression.

A. 7 less than a number B. the square of a number decreased by the product of 5 and the number

Example 2: Algebraic to Verbal Sentence

Write a verbal sentence to represent each equation.

A. B.

Example 3: Identify Properties of Equality

Name the property illustrated by each statement.

A. B.

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Example 4: Solve One-Step Equations Example 5: Solve a Multi-Step Equation

Solve 18 =1

2𝑡. Solve 53 = 3(𝑦 − 2) − 2(3𝑡 − 1).

Example 6: Solve for a variable.

GEOMETRY The formula for the surface are 𝑆 of a cone is 𝑆 = 𝜋𝑟𝑙 + 𝜋𝑟2, where 𝑙 is the slant height of

the cone and 𝑟 is the radius of the base. Solve the formula for 𝑙.

Standardized Test Example 7

If 4𝑔 + 5 =4

9, what is the value of 4𝑔 − 2?

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Lesson 1-5: Solving Inequalities Date:

The solution set of an inequality can be expressed by using .

Example 1: Solve an Inequality using Addition or Subtraction

Solve . Graph the solution set on a number line.

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Example 2: Solve an Inequality Using Multiplication or Division

Solve . Graph the solution set on a number line.

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Example 3: Solve Multi-Set Inequalities

Solve . Graph the solution set on a number line.

Example 4: Write and Solve an Inequality

CONSUMER COSTS Javier has at most $15.00 to spend today. He buys a bag of pretzels and a bottle of

juice for $1.59. If gasoline at this store costs $2.89 per gallon, how many gallons of gasoline,

to the nearest tenth of a gallon, can Javier buy for his car?

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Lesson 1-4: Solving Absolute Value Equations Date:

The of a number is its distance from 0 on a number line.

In mathematics, a is a condition that a solution must satisfy.

Even if the correct procedure for solving an equation is used, the answers may not be solutions to the

original problem. Such a number is called an .

Example 1: Evaluate an Expression with Absolute Value

Evaluate 10 – |2𝑎 + 7| if 𝑎 = – 1.5.

Example 2: Solve an Absolute Value Equation

Solve – 10 |𝑏 + 3| = – 40. Check your solutions.

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Example 3: No Solution

Solve |– 3𝑐 + 8| + 15 = 7.

Example 4: One Solution

Solve |𝑛 – 9| = 5𝑛 + 6. Check your solutions.

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Lesson 1-6: Solving Compound and Absolute Value Inequalities Date:

A consists of two inequalities joined by the word 𝑎𝑛𝑑 or

the word 𝑜𝑟.

The graph of a compound inequality containing 𝑎𝑛𝑑 is the of the solution

sets of the two inequalities.

The graph of a compound inequality containing 𝑜𝑟 is the of the solution sets of the two

inequalities.

Example 1: Solve an “And” Compound Inequality

Solve 10 ≤ 3𝑦 – 2 < 19. Graph the solution set on a number line.

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Example 2: Solve an “Or” Compound Inequality

Solve 𝑥 + 3 < 2 𝑜𝑟 – 𝑥 ≤ – 4. Graph the solution set on a number line.

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Example 3: Solve Absolute Value Inequalities

A. Solve 2 > |d|. Graph the solution set on a number line.

Example 4: Solve a Multi-Step Absolute Value Inequality

Solve |2𝑥 – 2| ≥ 4. Graph the solution set on a number line.

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Real-World Example 5: Write and Solve an Absolute Value Inequality

JOB HUNTING To prepare for a job interview, Hinda researches the position’s requirements and pay. She

discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ

from the average by as much as $2450.

A. Write an absolute value inequality to describe this situation.

B. Solve the inequality to find the range of Hinda’s starting salary. | 38,500 – 𝑥 | ≤ 2450