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4MA1/1H Jun 2025, Question 6: Solving Linear Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks

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The question, in short

Solve a linear equation with a fraction, showing algebraic working, then factorise a quadratic and use the result to solve the quadratic equation.

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

Part (a) · 3 marks

Solve x − 4 = (3 + 2x) ÷ 6 for x, showing clear algebraic working.

  1. 1Multiply both sides by 6: 6(x − 4) = 3 + 2x
  2. 26x − 24 = 3 + 2x
  3. 36x − 2x = 3 + 24
  4. 44x = 27
  5. 5x = 27/4 = 6.75

Answer27/4

Part (bi) · 2 marks

Factorise the quadratic expression y² − 11y + 30.

  1. 1Find two numbers with product 30 and sum −11
  2. 2−6 and −5
  3. 3y² − 11y + 30 = (y − 6)(y − 5)

Answer(y − 6)(y − 5)

Part (bii) · 1 mark

Using the factorisation, solve y² − 11y + 30 = 0.

  1. 1(y − 6)(y − 5) = 0
  2. 2y − 6 = 0 or y − 5 = 0
  3. 3y = 6 or y = 5

Answer6, 5

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

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