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0580/31 Oct/Nov 2025, Question 8: Solving Linear Equations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 5 marks

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The question, in short

Solve two linear equations for x and show the double inequality −4 ≤ x < 2 on a number line.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Find the value of x that satisfies 8x = 32.

  1. 1x = 32 ÷ 8 = 4

Answer4

Part (b) · 2 marks

Find the value of x that satisfies 6x − 3 = 12.

  1. 16x = 12 + 3 = 15
  2. 2x = 15 ÷ 6 = 2.5

Answer2.5

Part (c) · 2 marks

Draw −4 ≤ x < 2 on the given number line from −5 to 4, using correct endpoints.

  1. 1−4 is included (≤): draw a closed circle at −4
  2. 22 is not included (<): draw an open circle at 2
  3. 3Join the two circles with a line

AnswerClosed circle at −4 and open circle at 2, joined by a line

Stuck on a step? Read the free lesson: Solving Linear Equations

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Also searched as: 0580/31/O/N/25 · 0580_w25_qp_31 · 0580 w25 31 · question 8.
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