AlgebraExam Tips

Common Mistakes to Avoid

Part of Linear InequalitiesGCSE Mathematics

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 7 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 7

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.

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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