[discia] GCSE Maths › Algebra › Solving Inequalities

Solving Inequalities

discia.org 10 questions · 21 marks
Name Date
  1. Either paper 2 marks

    Write down all the integers that satisfy the inequality

    \(-4 ≤ m < 0\)

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    \(-4,\ -3,\ -2,\ -1\)
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  2. Either paper 2 marks

    Solve the inequality \(8x - 1 > 23\)

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    \(x > 3\)
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  3. Either paper 2 marks

    Solve the inequality \(4(x - 9) > -40\)

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    \(x > -1\)
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  4. Either paper 4 marks

    Two inequalities in \(m\) are set out in parts (a) and (b).

    (a)

    Solve \(4 ≤ 4m < 20\)

    (b)

    Solve \(4 < 4m ≤ 20\)

    (c)

    \(m\) is an integer.

    How are the integer solutions to part (a) and to part (b) different?

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    (a) \(1 ≤ m < 5\)
    (b) \(1 < m ≤ 5\)
    (c) Only (b) has \(5\) as a solution, and only (a) has \(1\) as a solution
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  5. Either paper 2 marks

    The solution of the inequality

    \(5x + b > 43\)

    is \(x > 7\).

    Work out the value of \(b\).

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    \(8\)
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  6. Either paper 2 marks

    Erin is asked to show the inequality \(1 \leq x < 5\) on a number line.

    Here is her attempt.

    -10123456789

    State the two mistakes she has made.

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    At the left end the mistake is the circle: it is drawn as an open circle at \(x = 1\), but it should be a filled-in circle at \(x = 1\). At the right end the mistake is the circle: it is drawn as a filled-in circle at \(x = 5\), but it should be an open circle at \(x = 5\).
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  7. Either paper 1 mark

    \(a < 0\) and \(b > 0\).

    Which of the statements below must always be true? Write it down.

    A: \(ab > 0\)

    B: \(a^2 < 0\)

    C: \(a - b > 0\)

    D: \(b - a > 0\)

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    b - a > 0
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  8. Either paper 1 mark

    \(6 < \sqrt{ x } < 7\)

    Circle the possible value of \(x\).

    \(2.55,\ 6.5,\ 13,\ 42\)

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    \(42\)
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  9. Either paper 2 marks

    Solve \(8x - 13 \le 5x + 2\)

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    \(x \le 5\)
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  10. Either paper 3 marks

    Solve \(1 ≤ 2x - 1 < 5\)

    Show answer
    \(1 ≤ x < 3\)
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discia.org Solving Inequalities · sheet 1
Answers Solving Inequalities · sheet 1
  1. \(-4,\ -3,\ -2,\ -1\)
  2. \(x > 3\)
  3. \(x > -1\)
  4. (a) \(1 ≤ m < 5\)
    (b) \(1 < m ≤ 5\)
    (c) Only (b) has \(5\) as a solution, and only (a) has \(1\) as a solution
  5. \(8\)
  6. At the left end the mistake is the circle: it is drawn as an open circle at \(x = 1\), but it should be a filled-in circle at \(x = 1\). At the right end the mistake is the circle: it is drawn as a filled-in circle at \(x = 5\), but it should be an open circle at \(x = 5\).
  7. b - a > 0
  8. \(42\)
  9. \(x \le 5\)
  10. \(1 ≤ x < 3\)
discia.org Solving Inequalities · sheet 1