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Inequalities Cambridge IGCSE Mathematics revision

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In plain words

An equation says two things are equal. An inequality says one is bigger. Instead of a single answer you get a whole range, such as "x is anything less than 4". You solve them exactly like equations, with one trap to watch for.

Three things to know

  1. Solve like an equation. But if you multiply or divide both sides by a negative number, turn the sign round.
  2. On a number line, an open circle means the end value is not included (< or >). A filled circle means it is (≤ or ≥).
  3. On a graph, the boundary line is dashed for < or > and solid for ≤ or ≥. Shade (or leave unshaded) the region the question asks for.

Worked example

Solve 3 − 2x < 9.

  1. Subtract 3 from both sides: −2x < 6.
  2. Divide both sides by −2, and turn the sign round.
  3. x > −3.

Tips and tricks

  • Dividing by a negative flips the sign. Check with a number: x = 0 gives 3 < 9, which is true, and 0 is greater than −3.
  • "List the integers" means whole numbers only, and watch which end is included.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Inequalities: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. Solve x + 4 > 9.
    • x > 13
    • x > 5 (the answer)
    • x < 5
    • x > 36

    Subtract 4 from both sides.

  2. Solve 3x ≤ 12.
    • x ≤ 36
    • x ≥ 4
    • x ≤ 4 (the answer)
    • x ≤ 9

    Divide both sides by 3.

  3. Solve −2x < 8.
    • x < −4
    • x > −4 (the answer)
    • x < 4
    • x > 4

    Dividing by −2 turns the sign round.

  4. Which integers satisfy 1 ≤ x < 4?
    • 2, 3
    • 1, 2, 3, 4
    • 1, 2, 3 (the answer)
    • 2, 3, 4

    1 is included; 4 is not.

  5. On a number line, what does a filled circle mean?
    • The value is not included.
    • The value is included. (the answer)
    • The value is negative.
    • The line stops.

    It goes with ≤ and ≥.

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