GCSE Mathematics Revision — Inequalities
Revise Inequalities for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP.
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- Inequalities in GCSE Mathematics: explanation, examples, and practice links on this page.
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What 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 examples
Worked example 1: Core method
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.
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Inequalities idea being tested, show the method or evidence, then explain why it answers the command word. This helps GCSE Mathematics students avoid memorising one surface pattern.
Worked example 3: Mark-scheme check
Finish by checking the answer against marks: one point for the correct Inequalities idea, one for accurate working or evidence, and one for a precise final statement. If any step is vague, rewrite it before moving to timed practice.
Mini lesson for Inequalities
1. Understand the core idea
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.
Can you explain Inequalities without copying the notes?
2. Turn it into marks
Solve -3 < 2x - 1 ≤ 5. Add 1 to all parts: -2 < 2x ≤ 6.
Underline the method, evidence, or command-word move that would earn credit in GCSE Algebra.
3. Fix the likely mark leak
Watch for this mistake: Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
Write one correction rule before doing another practice question.
Practise this topic
Start with low-focus cards for Inequalities, then move into full exam-style practice when you want the heavier session.
Mini quiz: Inequalities
Three quick checks for revision practice. They are original StudyVector prompts, not official exam-board questions.
Question 1
In one GCSE sentence, explain what Inequalities is testing.
Answer: 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.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Inequalities question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Forgetting to flip the inequality sign when multiplying or dividing by a negative number." What should their next repair task be?
Answer: Do one Inequalities question and review the mistake type.
Mark focus: Error correction and next-step practice.
Inequalities flashcards
Core idea
What is the main idea in 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.
Common mistake
What mistake should you avoid in Inequalities?
Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
Practice
What is one useful practice task for Inequalities?
Answer one Inequalities question and review the mistake type.
Exam board
How should you use board notes for Inequalities?
Use your own GCSE specification for exact paper wording and depth.
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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP 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.