# Graphing Solutions of Inequalities

Solving an inequality means describing a set, not just finding a number. This set is the solution set of the problem. To visualize the solution set, draw it on the number line. To do this, draw the number line and shade the part of the number line corresponding to the solution set. The solution set to a single inequality will be a half line that may or may not include the endpoint. When the endpoint is included, draw a solid dot for the endpoint. When the endpoint is not included, draw a circle.

Example 1

Represent the solution set of x 5 on a number line.

Solution

The solution set of x 5 is represented by the set of points to the left of 5 on the number line. It does include the endpoint, since x = 5 is included.

Example 2

Represent the solution set of x > 2 on a number line.

Solution

The solution set of x > 2 is a half line represented by the set of points to the right of 2 on the number line. It does not include the endpoint, since x = 2 is not included.