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More Lessons for Grade 9

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Videos, worksheets, solutions, and activities to help Algebra 1 students learn how to solve compound inequalities.

Compound Inequalities

Students learn that when solving a combined inequality in the form x is less than -3 or x is greater than 2, "or" means "union", or everything that's mentioned in the two inequalities. And when solving a combined inequality in the form x is less than negative 3 and x is greater than 2, "and" means "intersection", or only what's in common to the two inequalities.

So when graphing a combined inequality, the first step is to graph the inequalities above the number line, then combine them on the number line based on "or" (bring everything down to the number line) or "and" (only bring down the parts where the graphs overlap).

The problems in this lesson incorporate the ideas of solving inequalities and combined inequalities.

This video shows how to solve and graph compound inequalities. Shown are the and variety with the filled in line segment between the boundary points and the or variety with two outward arrows from the boundary points. It shows how to graph on a number line.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.