# Graphing Absolute Value Inequalities

How to graph absolute value inequalities: examples and their solutions.

## Example 1

Draw *y* = |*x*| - 2 using dashed lines.

(The inequality sign doesn't include '='.)

Graphing absolute value functions*y* is greater than the right side.

So color the upper region of the dashed graph.

## Example 2

Draw |*y*| = -|*x*| + 4 using solid lines.

(The inequality sign does include '='.)

Graphing absolute value functions*y* is lesser than the right side.

So color the region that includes

the lower region of the quadrant I graph.

There's another way to color the inequality.

Find a point that makes the inequality true: (0, 0).

|0| ≤ -|0| + 4 is true.

Then color the region that includes the point: (0, 0).