Download presentation

Presentation is loading. Please wait.

1
**Solving Absolute-Value Inequalities**

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

2
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.

4
**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 Since 2 is added to |x|, subtract 2 from both sides to undo the addition. |x| + 2 ≤ 6 –2 –2 |x| ≤ 4 Think, “The distance from x to 0 is less than or equal to 4 units.” –5 –4 –3 –2 –1 1 2 3 4 5 4 units x ≥ –4 AND x ≤ 4 Write as a compound inequality. –4 ≤ x ≤ 4

5
**Example 1B: Solving Absolute-Value Inequalities Involving <**

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 5 < –4 |x| – 5 < –4 Since 5 is subtracted from |x|, add 5 to both sides to undo the subtraction. |x| < 1 Think, “The distance from x to 0 is less than 1unit.” –2 –1 1 2 unit x is between –1 and 1. –1 < x AND x < 1 Write as a compound inequality. –1 < x < 1

6
**Example 1C: Solving Absolute-Value Inequalities Involving <**

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x + 4| – 1.5 < 3.5 |x + 4| – 1.5 < 3.5 Since 1.5 is subtracted from |x + 4|, add 1.5 to both sides to undo the subtraction. |x + 4| < 5 5 units Think, “The distance from x to –4 is less than 5 units.” –5 –4 –3 –2 –1 1 2 3 4 5 x + 4 > –5 AND x + 4 < 5 x + 4 is between –5 and 5. –4 – –4 –4 x > –9 AND x < 1

7
**Write as a compound inequality.**

Example 1C Continued x > –9 AND x < 1 Write as a compound inequality. –10 –8 –6 –4 –2 2 4 6 8 10 –9 < x < 1

8
**Think, “The distance from x to 0 is less than 3 units.”**

Check It Out! Example 1a Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| + 12 < 15 Since 12 is added to |x|, subtract 12 from both sides to undo the addition. |x| + 12 < 15 – 12 –12 |x| < 3 –5 –4 –3 –2 –1 1 2 3 4 5 3 units Think, “The distance from x to 0 is less than 3 units.” x is between –3 and 3. x > –3 AND x < 3 Write as a compound inequality. –3 < x < 3

9
**Think, “The distance from x to 0 is less than 1 unit.”**

Check It Out! Example 1b Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 6 < –5 Since 6 is subtracted from |x|, add 6 to both sides to undo the subtraction. |x| – 6 < –5 |x| < 1 1 unit Think, “The distance from x to 0 is less than 1 unit.” –2 –1 1 2 x is between –1 and 1. x > –1 AND x < 1 Write as a compound inequality. –1 < x < 1

10
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.

12
**Example 2A: Solving Absolute-Value Inequalities Involving >**

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| + 2 > 7 |x| + 2 > 7 Since 2 is added to |x|, subtract 2 from both sides to undo the addition. – 2 –2 |x| > 5 5 units –10 –8 –6 –4 –2 2 4 6 8 10 x < –5 OR x > 5 Write as a compound inequality.

13
**Example 2B: Solving Absolute-Value Inequalities Involving >**

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 12 ≥ –8 Since 12 is subtracted from |x|, add 12 to both sides to undo the subtraction. |x| – 12 ≥ –8 |x| ≥ 4 4 units –10 –8 –6 –4 –2 2 4 6 8 10 x ≤ –4 OR x ≥ 4 Write as a compound inequality.

14
**Example 2C: Solving Absolute-Value Inequalities Involving >**

Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x + 3| – 5 > 9 |x + 3| – 5 > 9 Since 5 is subtracted from |x + 3|, add 5 to both sides to undo the subtraction. |x + 3| > 14 14 units –16 –12 –8 –4 4 8 12 16 x + 3 < –14 OR x + 3 > 14

15
**Solve the two inequalities. – 3 –3 –3 –3**

Example 2C Continued x + 3 < –14 OR x + 3 > 14 Solve the two inequalities. – – –3 –3 x < –17 OR x > 11 –24 –20 –16 –12 –8 –4 4 8 12 16 –17 11 Graph.

16
**Write as a compound inequality.**

Check It Out! Example 2a Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| + 10 ≥ 12 |x| + 10 ≥ 12 Since 10 is added to |x|, subtract 10 from both sides to undo the addition. – 10 –10 |x| ≥ 2 2 units –5 –4 –3 –2 –1 1 2 3 4 5 x ≤ –2 OR x ≥ 2 Write as a compound inequality.

17
**Write as a compound inequality.**

Check It Out! Example 2b Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 7 > –1 |x| – 7 > –1 Since 7 is subtracted from |x|, add 7 to both sides to undo the subtraction. |x| > 6 6 units –10 –8 –6 –4 –2 2 4 6 8 10 x < –6 OR x > 6 Write as a compound inequality.

18
Check It Out! Example 2c Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. Since is added to |x |, subtract from both sides to undo the addition. 3.5 units –5 –4 –3 –2 –1 1 2 3 4 5 OR

19
**Check It Out! Example 2c Continued**

OR Solve the two inequalities. OR –10 –8 –6 –4 –2 2 4 6 8 10 1 Graph.

Similar presentations

OK

Lesson 5 Contents Glencoe McGraw-Hill Mathematics Algebra 2005 Example 1Solve an Absolute Value Equation Example 2Write an Absolute Value Equation.

Lesson 5 Contents Glencoe McGraw-Hill Mathematics Algebra 2005 Example 1Solve an Absolute Value Equation Example 2Write an Absolute Value Equation.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on producers consumers and decomposers worksheets Ppt on water activity symbol Ppt on classical economics school Ppt on immunization schedule in india Laser video display ppt on tv Ppt on electricity for class 10th roll Ppt on trial and error supernatural Ppt on peak load pricing economics Ppt on telephone exchange in indian railways Ppt on related party transactions as per companies act 2013