How to Solve Linear Inequalities — Step by Step Guide

Step-by-Step Method

1. 1

   Treat the inequality like an equation — add, subtract, multiply, divide on both sides.

2. 2

   IMPORTANT: When you multiply or divide by a negative number, flip the inequality sign.

3. 3

   Express the solution as an interval or on a number line.

4. 4

   Open circle (○) for strict inequality (<, >) and closed circle (●) for inclusive (≤, ≥).

5. 5

   For compound inequalities, solve each part separately and find the intersection.

Worked Example

Common Mistakes to Avoid

• ✗

  Forgetting to reverse the inequality sign when dividing by a negative number.

• ✗

  Using the wrong circle (open vs closed) on the number line.

• ✗

  Not checking the solution by substituting a value from the solution set.

• ✗

  Confusing 'and' (intersection) with 'or' (union) in compound inequalities.

Practice Linear Inequalities on SparkEd

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Frequently Asked Questions

How do I solve Linear Inequalities problems?

Treat the inequality like an equation — add, subtract, multiply, divide on both sides. IMPORTANT: When you multiply or divide by a negative number, flip the inequality sign.

What are common mistakes in Linear Inequalities?

Forgetting to reverse the inequality sign when dividing by a negative number. Using the wrong circle (open vs closed) on the number line.

Which class covers Linear Inequalities?

Linear Inequalities is typically taught in Class 9, 10. SparkEd has free practice for all these grades.

Where can I practise Linear Inequalities for free?

SparkEd offers free chapter-wise practice for Linear Inequalities aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.