Discia GCSE Maths › Algebra › Inequalities

Inequalities worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 25 marks Sheet 1
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  1. 2 marks

    Here is an inequality.

    A number line with an open circle and the region to the right shaded-11-10-9-8-7-6-5-4-3-2-1

    Write down the inequality shown.

  2. 2 marks

    Solve \(4x + 4 > 32\)

  3. 3 marks

    Here is an inequality.

    A number line with a filled circle and the region to the left shaded-4-3-2-10123456
    (a)

    Write down the inequality shown.

    (b)

    State the largest integer that satisfies this inequality.

  4. 3 marks A number line with a shaded region between two open circles-1012345678910

    \(n\) is an integer and \(0 < n < 5\).

    Write down all the possible values of \(n\).

  5. 2 marks

    The solution of the inequality

    \(4x + b > -24\)

    is \(x > -3\).

    Calculate the value of \(b\).

  6. 3 marks

    Solve \(-6x - 6 < 6\)

  7. 2 marks

    Here is an inequality.

    A number line with an open circle and the region to the right shaded-2-1012345678

    Write down the inequality shown.

  8. 2 marks

    Solve \(4x + 9 > 37\)

  9. 3 marks

    Here is an inequality.

    A number line with a filled circle and the region to the left shaded-10123456789
    (a)

    Write down the inequality shown.

    (b)

    Write down the largest integer that satisfies this inequality.

  10. 3 marks A number line with a shaded region between two open circles-4-3-2-101234567

    \(n\) is an integer and \(-2 < n < 3\).

    List all the possible values of \(n\).

Answers

  1. \(x > -5\)
  2. \(x > 7\)
  3. (a) \(x \leq 2\)
    (b) \(2\)
  4. \(1, 2, 3, 4\)
  5. \(-12\)
  6. \(x > -2\)
  7. \(x > 4\)
  8. \(x > 7\)
  9. (a) \(x \leq 2\)
    (b) \(2\)
  10. \(-1, 0, 1, 2\)

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