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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.

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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.

  1. 1Add 2 to both sides: 3x > 9.
  2. 2Divide both sides by 3: x > 3.
  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

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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.

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Key terms explained

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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).

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