Equations and Inequalities: Graphing Single–Variable Inequalities

An inequality compares two expressions using an inequality sign.
-  Inequality signs are: “less than" , "greater than" , “less than or equal to” , and “greater than or equal to” .
-  To graph a single–variable inequality, find the value of the inequality on the number line.
-  For less than () or greater than () draw an open circle on the value of the variable. If there is an equal sign too, then use a filled circle.
-  Draw an arrow to the right for greater or to the left for less than.

Examples:

Example 1. Draw a graph for this inequality.

Solution: Since the variable is greater than 2, then we need to find 2 in the number line and draw an open circle on it. Then, draw an arrow to the right.
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Example 2. Graph this inequality. .

Solution: Since the variable is less than or equal to , then we need to find on the number line and draw a filled circle on it. Then, draw an arrow to the left.