3-6 Compound Inequalities

Objectives

To solve and graph inequalities containing the word and To solve and graph inequalities containing the word or

Image Long Description

The Solve It involves a value that is between two numbers. You can use a compound inequality to represent this relationship. A compound inequality consists of two distinct inequalities joined by the word and or the word or.

Essential Understanding You find the solutions of a compound inequality either by identifying where the solution sets of the distinct inequalities overlap or by combining the solution sets to form a larger solution set.

The graph of a compound inequality with the word and contains the overlap of the graphs of the two inequalities that form the compound inequality.

Image Long Description

The graph of a compound inequality with the word or contains each graph of the two inequalities that form the compound inequality.

Image Long Description

You can rewrite a compound inequality involving and as a single inequality. For instance, in the inequality above, you can write x ≥ 3 x greater than or equal to 3  and x ≤ 7 x less than or equal to 7  as 3 ≤ x ≤ 7 . 3 less than or equal to x less than or equal to 7 .  You read this as “x is greater than or equal to 3 and less than or equal to 7.” Another way to read it is “x is between 3 and 7, inclusive.” In this example, inclusive means the solutions of the inequality include both 3 and 7.

Table of Contents