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AlgebraExam Tips

Common Mistakes to Avoid

Part of Linear Inequalities · GCSE GCSE Mathematics revision

This exam tips covers Common Mistakes to Avoid 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 7 of 8 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.

Topic position

Section 7 of 8

Practice

14 questions

Recall

11 flashcards

Common Mistakes to Avoid

Wrong: -2x > 6 becomes x > -3
Right: -2x > 6 becomes x < -3 (flip when dividing by negative!)
Wrong: Using closed circle for x < 5
Right: Open circle for < and >, closed for ≤ and ≥
Wrong: Integer solutions for -2 < x ≤ 3 include -2
Right: -2 is NOT included (strict <), integers are -1, 0, 1, 2, 3

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.

Worked Example 3: Compound InequalityKnowledge Organiser: Linear InequalitiesNot Just Equals!The Four Inequality Symbols

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.

14 questions on Linear Inequalities — practise free

Instant marking, adaptive difficulty, and 11 spaced repetition flashcards. Free until your GCSEs.

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Worked Example 3: Compound Inequality

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Knowledge Organiser: Linear Inequalities