Absolute Value Inequalities

SEI.3.AC.1SLE 1: Solve, with and without appropriate technology, multi-step equations and inequalities with

rational coefficients numerically, algebraically and graphically

Students will be able to solve absolute value equations and inequalities, and be able to graph them.

FHS Equations and Inequalities 2

Absolute Value Inequalities

To solve absolute value inequalities, we convert them to compound inequalities.

If we have an inequality like |x| > 5, we convert that to an “or” compound inequality. [Think “great”or”]

That would be: x > 5 or x < – 5.

FHS Equations and Inequalities 3

Absolute Value Inequalities

If we have an inequality like |x| < 5, we convert that to an “and” compound inequality. [Think less th“and”]

That would be: x < 5 and x > – 5.

We can then combine the two equations to become a single inequality:

5 5x

FHS Equations and Inequalities 4

| | | | | | | -4 -3 -2 -1 0 1 2

Examples

Solve the following inequality and graph your answer on the number line given:

2 3 5x 3 3

1x 2 2x

Set up two inequalities with an “or” between them.

Then we can graph the answer.

1 1 x or x

FHS Equations and Inequalities 5

Examples

Solve the following inequality and graph your answer on the number line given:

3 1 12 x

5 3 x and x1 4x Set up two

inequalities with an “and” between them.

Then we can graph the answer.

| | | | | | | | | | -3 -2 -1 0 1 2 3 4 5 6

3 5x

1 4 1 4 x and x

Combine these into one.