1. Chapter 2: Equations and Inequalities
Section 2.7: Absolute Value Inequalities

2. Section 2.7: Absolute Value Inequalities
Goal: To solve inequalities involving absolute value and graph the solution sets

3. Section 2.7: Absolute Value Inequalities
Remember:
And: Graph the intersection of the two graphs
Answers can include 
Or: Graph the union of the two graphs (include everything in final graph)
Answers can include

4. Section 2.7: Absolute Value Inequalities
An absolute value inequality can be solved by rewriting it as a compound inequality.
For all real numbers a and b, b > 0, the following statements are true:
If |a| < b, then a < b AND a > -b
If |2x + 1| < 5, then 2x + 1 < 5 AND 2x + 1 > -5
If |a| > b, then a > b OR a < -b
If |2x + 1| > 5, then 2x + 1 > 5 OR 2x + 1 < -5
These statements are also true for ≤ and ≥

5. Section 2.7: Absolute Value Inequalities
Example
Solve |2x – 2| ≥ 4. Graph the solution set on a number line.
Solve |½ x – 5| - 8 ≥ Graph the solution set on a number line

6. Section 2.7: Absolute Value Inequalities
Example
Solve |3x -11| + 12 ≤ 10. Graph the solution set on a number line
Solve 3 |2x + 4| – 15 ≤ 21 Graph the solution set on a number line

7. Section 2.7: Absolute Value Inequalities
Homework:
Pg. 79: Practice Exercises #10-34 (even)