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Chapter 2: Equations and Inequalities

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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)


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