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4024/12 May/Jun 2022, Question 24: Solving Linear Equations

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Solve an equation with a fraction equal to 3, then combine two algebraic fractions into one simplified fraction.

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

Part (a) · 3 marks

Solve (2 − 5x)/(3x + 10) = 3 for x.

  1. 12 − 5x = 3(3x + 10)
  2. 22 − 5x = 9x + 30
  3. 32 − 30 = 9x + 5x
  4. 4−28 = 14x
  5. 5x = −2

Answer−2

Part (b) · 3 marks

Write 3/(x − 2) − 5/(2x + 1) as a single fraction in simplest form.

  1. 1Common denominator (x − 2)(2x + 1)
  2. 2= [3(2x + 1) − 5(x − 2)]/((x − 2)(2x + 1))
  3. 3= (6x + 3 − 5x + 10)/((x − 2)(2x + 1))
  4. 4= (x + 13)/((x − 2)(2x + 1))

Answer(x + 13)/((x − 2)(2x + 1)) or (x + 13)/(2x² − 3x − 2)

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

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