Linear Inequality 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 use the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line.

How to solve a linear inequality and graph the solution on the number line?

Solving a linear inequality is very similar to solving a linear equation. The main difference is that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

Here’s a step-by-step guide:

1. Simplify both sides: Combine like terms on each side of the inequality.
2. Isolate the variable: Use inverse operations (addition, subtraction, multiplication, or division) to get the variable alone on one side of the inequality.
3. Reverse the inequality sign (if necessary): If you multiply or divide both sides by a negative number, reverse the inequality sign.

Graphing the Solution on a Number Line:

1. Locate the critical point: This is the value that makes the inequality true or false.
2. Determine the direction of the shading:

• If the inequality is “greater than” or “greater than or equal to,” shade to the right of the critical point.
• If the inequality is “less than” or “less than or equal to,” shade to the left of the critical point.

3. Choose the appropriate endpoint:

• If the inequality includes “equal to,” use a closed circle (●) to indicate that the endpoint is included in the solution.
• If the inequality does not include “equal to,” use an open circle (○) to indicate that the endpoint is not included in the solution.

Have a look at this video if you need to review how to solve linear inequalities and graph the solutions on a number line.

• Solving Inequalities In One Variable & Graph On Number Line

Click on the following worksheet to get a printable pdf document.
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More Linear Inequality Worksheetss

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(Answers on the second page.)
Linear Inequality Worksheets #1
Linear Inequality Worksheets #2

Related Lessons & Worksheets

Solving Inequalities

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One-step Inequality
Two-step Inequality

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