1. Solving Absolute Value Inequalities

2. when you have: less than (< or ≤):we write it as a “sandwich” |x + 1|< 3 -3 < x + 1 < 3 greater than (> or ≥): we write it as an “or” |x + 1| > 3 x + 1 > 3 or x + 1 < -3 Remember as: –less “and” –great “or”

3. Solving Absolute Value Inequalities Isolate the absolute value first –(get it by itself) make it an “and” or an “or” statement solve and graph

4. Example |x| ≥ 6

5. Example |x| ≤ 0.5

6. Example |x - 5| ≥ 7

7. Example |-4x - 5| + 3 < 9

8. Example 3|5m - 6| - 8 ≤ 13

9. Solving Inequalities one-step and multi-step inequalities –follow the steps for solving an equation –reverse the inequality symbol when multiplying/dividing by a negative number compound inequalities –rewrite as two separate inequalities, if necessary absolute value inequalities –isolate the absolute value expression on one side of the inequality –rewrite as a compound inequality, then solve