Solving Absolute Value Inequalities

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