IGCSE Math RevisionWorked example 1: Solving an inequality
Solve \(4x-3\le13\).
Solution
- Add 3: \(4x\le16\).
- Divide by 4: \(x\le4\).
Answer: \(x\le4\)
Tip: Only reverse the sign when multiplying or dividing by a negative.
Edexcel IGCSE Maths (4MA1) · Unit 2: Algebra Basics
IGCSE Maths Inequalities Questions and Answers
Inequalities questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then cover each solution and redo it yourself.
- 3 worked examples
- Higher tier · calculator allowed
- Free, no sign-in
What this topic covers
- Linear Inequalities 1: Solving one- and two-step linear inequalities.
- Linear Inequalities 2: Inequalities with variables on both sides.
- Quadratic Inequalities (algebra & graphs): Solving quadratic inequalities graphically and algebraically.
Inequalities worked examples
Worked example 2: Double inequality
Solve \(-3<2x+1\le9\) and list the integer solutions.
Solution
- Subtract 1 throughout: \(-4<2x\le8\).
- Divide by 2: \(-2<x\le4\).
- Integers: \(-1,0,1,2,3,4\).
Answer: \(-2<x\le4\); −1, 0, 1, 2, 3, 4
Tip: −2 is not included because the inequality is strict.
Worked example 3: Quadratic inequality
Solve \(x^2-5x+4\le0\).
Solution
- Factorise: \((x-1)(x-4)\le0\).
- Critical values 1 and 4; the curve is below the axis between them.
- \(1\le x\le4\).
Answer: \(1\le x\le4\)
Tip: Sketch the parabola to decide which part you need.
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Revise inequalities for the exam
- Unit 2 practice: Algebra Basics in the student hub (more questions with mark schemes)
- IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
- Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
- IGCSE Maths 4MA1 examiner report summary: where students lose marks
Questions students ask
Which Edexcel IGCSE Maths papers test inequalities?
Either Higher tier paper, 1H or 2H, can test inequalities: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more inequalities questions?
In the IGCSE student hub: Unit 2 (Algebra Basics) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.