Chapter 2: Equations and InequalitiesSection 2.7: Absolute Value Inequalities

Section 2.7: Absolute Value Inequalities Goal: To solve inequalities

involving absolute value and graph the solution sets

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

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 ≥

Section 2.7: Absolute Value Inequalities

Example ◦Solve |2x – 2| ≥ 4. Graph the solution

set on a number line.

Example ◦Solve |½ x – 5| - 8 ≥ -20. Graph the

solution set on a number line

Section 2.7: Absolute Value Inequalities

Example ◦Solve |3x -11| + 12 ≤ 10. Graph the

solution set on a number line

Example ◦Solve 3 |2x + 4| – 15 ≤ 21 Graph the

solution set on a number line

Section 2.7: Absolute Value Inequalities Homework:

◦Pg. 79: Practice Exercises #10-34 (even)