Solve & Graph Compound Inequalities Worksheets
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Algebra I Math Lessons
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 solve two inequalities joined by “and” or “or” and then graph the solution set on the number line.
How to Solve and Graph Compound Inequalities?
A compound inequality is a combination of two or more inequalities. There are two main types: “and” and “or” inequalities.
“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 when graphing compound inequalities:
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 solve & graph compound inequalities.
Click on the following worksheet to get a printable pdf document.
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Related Lessons & Worksheets
Solving & Graphing Inequalities
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One-step Inequality
Two-step Inequality
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