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AlgebraDeep Dive

Solving Inequalities (Like Equations!)

Part of Linear Inequalities — GCSE Mathematics

This deep dive covers Solving Inequalities (Like Equations!) within Linear Inequalities for GCSE Mathematics. Revise Linear Inequalities in Algebra for GCSE Mathematics with 14 exam-style questions and 11 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 3 of 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 7

Practice

14 questions

Recall

11 flashcards

Solving Inequalities (Like Equations!)

  1. Same rules as equations: add, subtract, multiply, divide both sides
  2. Keep the inequality sign pointing the same way... EXCEPT:
  3. When multiplying/dividing by a NEGATIVE, FLIP the sign!
  4. Simplify until you have x on its own
  5. Check: pick a value in your solution and verify it works

Keep building this topic

Read this section alongside the surrounding pages in Linear Inequalities. That gives you the full topic sequence instead of a single isolated revision point.

The Four Inequality SymbolsWorked Example 1: Simple InequalityNot Just Equals!Worked Example 2: Negative Coefficient (FLIP!)

Practice Questions for Linear Inequalities

Which of the following correctly describes how to represent x > 3 on a number line?

  • A. A closed (filled) circle at 3, with an arrow pointing to the right
  • B. An open (empty) circle at 3, with an arrow pointing to the right
  • C. An open (empty) circle at 3, with an arrow pointing to the left
  • D. A closed (filled) circle at 3, with an arrow pointing to the left
1 markfoundation

When solving an inequality, the direction of the inequality sign must reverse if you multiply or divide both sides by a negative number. Explain why this rule is necessary. You may use an example to support your explanation.

2 marksstandard

Quick Recall Flashcards

The Flip Rule for inequalities
When you multiply or divide BOTH sides by a NEGATIVE number, you MUST reverse (flip) the inequality sign. Example: -2x > 6 becomes x < -3
Open vs Closed Circle on a number line
Open circle (hollow) for < and > — endpoint NOT included. Closed circle (filled) for ≤ and ≥ — endpoint IS included.

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The Four Inequality Symbols

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Worked Example 1: Simple Inequality