Graphing Compound Inequalities on a Number Line Worksheets

Printable “Linear Inequality” worksheets:
Solve 1-step inequalities (addition & subtraction)
Solve 1-step inequalities (multiplication & division)
Solve 1-step inequalities (all operations)
Solve linear inequalities (include number lines)
Graph compound inequalities on the number line
Solve & graph compound inequalities

Solve & graph inequalities with two variables

Examples, solutions, videos, and worksheets to help Grade 8 students learn how to graph the solution set of two compound inequalities joined by either “and” or “or” and graph the solution set on the number line

How to Graph Compound Inequalities on a Number Line?

To graph a compound inequality on a number line, we need to visualize the solution set for each inequality and then combine them based on the “and” or “or” condition.

“And” Inequalities
An “and” inequality is true only when both inequalities are true. The solution set is the intersection of the two individual solution sets.
An “and” compound inequality is written as something like:
𝑎 < 𝑥 < 𝑏
or
𝑎 < 𝑥 and 𝑥 < 𝑏
This means that 𝑥 x must satisfy both inequalities.

“Or” Inequalities
An “or” inequality is true when either inequality is true. The solution set is the union of the two individual solution sets.
An “or” compound inequality is written as:
𝑥 < 𝑎 or 𝑥 > 𝑏
This means that 𝑥 can satisfy either inequality.

Key Points:
Open circles (○) indicate that the endpoint is not included in the solution.
Closed circles (●) indicate that the endpoint is included in the solution.
For “and” inequalities, the solution is the overlap of the shaded regions.
For “or” inequalities, the solution is the combination of the shaded regions.

Have a look at this video if you need to review how to graph a compound inequality on a number line.

• How to Graph Compound Inequalities on a Number Line

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