Solve the compound inequality: -3x < 6 or x + 4 < 2. Graph the solution set on a number line.

x > -2 or x < -2. The graph should show an open circle at -2, with shading to the left and to the right (excluding -2).

Solving Compound Inequalities

9th Grade•50 minutes

I can solve compound inequalities and graph the solution sets on a number line.

A compound inequality consists of two inequalities considered together, which can be an intersection or a union.

An intersection uses the word and, meaning the solution must be true for both inequalities, representing where the graphs overlap.

A union uses the word or, meaning the solution must be true for at least one inequality, representing wherever the inequalities are shown on a graph.

This lesson includes 6 practice questions to reinforce learning.

View questions preview

1. Which statement best describes the key difference when solving compound inequalities involving 'and' versus 'or'?

2. Solve the compound inequality: 2 < x + 1 ≤ 5. Graph the solution set on a number line.

3. Which of the following compound inequalities has no solution?

...and 3 more questions

5.4 Solving Compound Inequalities

Megan Tompkins