IGCSE Maths Inequalities Notes
Inequalities compare quantities that are not equal. Solve them like equations, but flip the sign when multiplying or dividing by a negative.
Key concepts
- Inequality symbols
- <, ≤, >, ≥ show 'less than', 'less than or equal to', and so on.
- Sign flip
- Multiplying or dividing both sides by a negative reverses the inequality.
- Number line
- Open circle for strict (<, >), filled circle for inclusive (≤, ≥).
Key formulas
Solving rule
same operation both sides
Flip the symbol when ×/÷ by a negative.
Worked example
Solve 3x − 2 > 7.
- 1Add 2 to both sides: 3x > 9.
- 2Divide both sides by 3: x > 3.
- 3Since dividing by a positive, the symbol stays the same.
Answer: x > 3
Common mistakes
✗ Not flipping the sign when dividing by a negative.
✓ Reverse < to > (and vice versa) whenever you ×/÷ by a negative.
✗ Wrong circle type on a number line.
✓ Open for < or >, filled for ≤ or ≥.
✗ Only giving integer answers when a range is required.
✓ State the full solution set, e.g. x > 3.
Quick check
Try these, then reveal the answers.
Solve x + 4 < 10.Reveal answer
x < 6
Solve −2x > 6.Reveal answer
x < −3
Open or filled circle for x ≥ 2?Reveal answer
Filled
Exam tips
- Treat the inequality like an equation, watching for the sign flip.
- List integer solutions carefully if the question asks for them.
- Draw number lines neatly with the correct open/filled circles.
Related practice
Practise this topic
Exam-style questions with instant Gradion feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Gradion
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Frequently asked questions
When do I flip the inequality sign?+
Whenever you multiply or divide both sides by a negative number.
What is the difference between < and ≤?+
< means strictly less than (value excluded); ≤ means less than or equal to (value included).
Create a free account to practise inequalities with Gradion feedback
Try 5 questions now, get instant examiner-grade marking and ask the Gradion to explain anything. Free during our early launch period — no credit card required.