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.
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
Practice questions for Linear Inequalities
Which of the following correctly describes how to represent x > 3 on a number line?
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.
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.