Inequalities — GCSE Mathematics Revision
Revise Inequalities for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Direct & Inverse ProportionWhat is Inequalities?
Inequalities use the symbols <, >, ≤, ≥ instead of =. You solve them like equations, but with one critical rule: when you multiply or divide both sides by a negative number, you must reverse the inequality sign. You can represent solutions on a number line (open circle for < or >, closed circle for ≤ or ≥) and need to solve double inequalities like 3 < 2x + 1 ≤ 9.
Step-by-step explanationWorked example
Solve -3 < 2x - 1 ≤ 5. Add 1 to all parts: -2 < 2x ≤ 6. Divide all parts by 2: -1 < x ≤ 3. Integer solutions: 0, 1, 2, 3.
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Common mistakes
- 1Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
- 2Using the wrong circle on the number line — open for strict (< or >), filled for inclusive (≤ or ≥).
- 3Not listing all integer values when the question asks for integers satisfying an inequality.
- 4Treating a double inequality as two separate problems and losing the connection between the bounds.
Inequalities exam questions
Exam-style questions for Inequalities with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Inequalities
Core concept
Inequalities use the symbols <, >, ≤, ≥ instead of =. You solve them like equations, but with one critical rule: when you multiply or divide both sides by a negative number, you must reverse the inequ…
Frequently asked questions
When do I flip the inequality sign?
Only when you multiply or divide both sides by a negative number. Adding or subtracting negatives does NOT require flipping.
How do I show inequalities on a number line?
Draw an open circle for < or > (not included) and a filled circle for ≤ or ≥ (included). Shade the region between or beyond the circles.