+ All Categories
Home > Documents > Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities...

Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities...

Date post: 27-Mar-2015
Category:
Upload: john-spencer
View: 230 times
Download: 0 times
Share this document with a friend
Popular Tags:
19
Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentatio n
Transcript
Page 1: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities3-Ext Solving Absolute-Value Inequalities

Holt Algebra 1

Lesson Presentation

Page 2: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

When an inequality contains an absolute-value expression, it can be written as a compound inequality. The inequality |x| < 5 describes all real numbers whose distance from 0 is less than 5 units. The solutions are all numbers between –5 and 5, so |x|< 5 can be written as –5 < x < 5, which is the compound inequality x > –5 AND x < 5.

Page 3: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Page 4: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Example 1A: Solving Absolute-Value Inequalities Involving <

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

|x| + 2 ≤ 6

|x| + 2 ≤ 6–2 –2

|x| ≤ 4

x ≥ –4 AND x ≤ 4

–5 –4 –3 –2 –1 0 1 2 3 4 5

4 units 4 units

–4 ≤ x ≤ 4

Since 2 is added to |x|, subtract 2 from both sides to undo the addition.

Think, “The distance from x to 0 is less than or equal to 4 units.”

Write as a compound inequality.

Page 5: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

|x| – 5 < –4

|x| – 5 < –4+5 +5|x| < 1

–1 < x AND x < 1

–1 < x < 1

Since 5 is subtracted from |x|, add 5 to both sides to undo the subtraction.

Think, “The distance from x to 0 is less than 1unit.”

x is between –1 and 1.Write as a compound inequality.

–2 –1 0 1 2

unit1

unit1

Example 1B: Solving Absolute-Value Inequalities Involving <

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

Page 6: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

|x + 4| – 1.5 < 3.5

|x + 4| – 1.5 < 3.5+1.5 +1.5

|x + 4| < 5

Since 1.5 is subtracted from |x + 4|, add 1.5 to both sides to undo the subtraction.

Think, “The distance from x to –4 is less than 5 units.”

x + 4 > –5 AND x + 4 < 5 x + 4 is between –5 and 5.

–5 –4 –3 –2 –1 0 1 2 3 4 5

Example 1C: Solving Absolute-Value Inequalities Involving <

–4 –4 –4 –4

x > –9 AND x < 1

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

5 units 5 units

Page 7: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

x > –9 AND x < 1

–9 < x < 1

–10 –8 –6 –4 –2 0 2 4 6 8 10

Write as a compound inequality.

Example 1C Continued

Page 8: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Check It Out! Example 1a

|x| + 12 < 15

|x| + 12 < 15– 12 –12

|x| < 3

Since 12 is added to |x|, subtract 12 from both sides to undo the addition.

Think, “The distance from x to 0 is less than 3 units.”

x is between –3 and 3.x > –3 AND x < 3

–3 < x < 3

Write as a compound inequality.

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

–5 –4 –3 –2 –1 0 1 2 3 4 5

3 units 3 units

Page 9: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Check It Out! Example 1b

|x| – 6 < –5

|x| – 6 < –5+ 6 +6

|x| < 1

Since 6 is subtracted from |x|, add 6 to both sides to undo the subtraction.

Think, “The distance from x to 0 is less than 1 unit.”–2 –1 0 1 2

x > –1 AND x < 1

–1 < x < 1

x is between –1 and 1.

Write as a compound inequality.

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

1 unit 1 unit

Page 10: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

The inequality |x| > 5 describes all real numbers whose distance from 0 is greater than 5 units. The solutions are all numbers less than –5 or greater than 5. The inequality |x| > 5 can be written as the compound inequality x < –5 OR x > 5.

Page 11: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Page 12: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

Example 2A: Solving Absolute-Value Inequalities Involving >

|x| + 2 > 7|x| + 2 > 7

– 2 –2

|x| > 5

x < –5 OR x > 5

Since 2 is added to |x|, subtract 2 from both sides to undo the addition.

Write as a compound inequality.

–10 –8 –6 –4 –2 0 2 4 6 8 10

5 units 5 units

Page 13: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

|x| – 12 ≥ –8|x| – 12 ≥ –8

+ 12 +12

|x| ≥ 4

–10 –8 –6 –4 –2 0 2 4 6 8 10

x ≤ –4 OR x ≥ 4

Since 12 is subtracted from |x|, add 12 to both sides to undo the subtraction.

Write as a compound inequality.

Example 2B: Solving Absolute-Value Inequalities Involving >

4 units 4 units

Page 14: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

Example 2C: Solving Absolute-Value Inequalities Involving >

|x + 3| – 5 > 9

|x + 3| – 5 > 9+ 5 +5

|x + 3| > 14

Since 5 is subtracted from |x + 3|, add 5 to both sides to undo the subtraction.

–16 –12 –8 –4 0 4 8 12 16

x + 3 < –14 OR x + 3 > 14

14 units 14 units

Page 15: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

– 3 –3 –3 –3

x < –17 OR x > 11

Solve the two inequalities.

–24 –20 –16 –12 –8 –4 0 4 8 12 16

–17 11Graph.

Example 2C Continued

x + 3 < –14 OR x + 3 > 14

Page 16: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Check It Out! Example 2a

|x| + 10 ≥ 12

|x| + 10 ≥ 12– 10 –10

|x| ≥ 2

–5 –4 –3 –2 –1 0 1 2 3 4 5

x ≤ –2 OR x ≥ 2 Write as a compound inequality.

Since 10 is added to |x|, subtract 10 from both sides to undo the addition.

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

2 units 2 units

Page 17: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Check It Out! Example 2b

|x| – 7 > –1

|x| – 7 > –1+7 +7

|x| > 6

–10 –8 –6 –4 –2 0 2 4 6 8 10

x < –6 OR x > 6

Since 7 is subtracted from |x|, add 7 to both sides to undo the subtraction.

Write as a compound inequality.

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

6 units 6 units

Page 18: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Check It Out! Example 2c

–5 –4 –3 –2 –1 0 1 2 3 4 5

Since is added to |x + 2 |, subtract from both sides to undo the addition.

OR

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

3.5 units 3.5 units

Page 19: Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation.

Holt Algebra 1

3-Ext Solving Absolute-Value Inequalities

Check It Out! Example 2c Continued

OR

OR

–10 –8 –6 –4 –2 0 2 4 6 8 10

1

Solve the two inequalities.

Graph.


Recommended