Solving Absolute Value Inequalities

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”

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

Example |x| ≥ 6

Example |x| ≤ 0.5

Example |x - 5| ≥ 7

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

Example 3|5m - 6| - 8 ≤ 13

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