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0606/12 Feb/Mar 2026, Question 6: Modulus Equations and Inequalities

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Solve an absolute value equation and an absolute value inequality involving linear expressions in x.

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Part (a) · 3 marks

Find the values of x satisfying |3x + 2| = 7.

  1. 13x + 2 = 7 or 3x + 2 = −7
  2. 2x = 5/3 or x = −3

Answerx = 5/3, x = −3

Part (b) · 4 marks

Find the range of x values satisfying |2x − 4| > |x + 1|.

  1. 1Square both sides: (2x − 4)² > (x + 1)²
  2. 24x² − 16x + 16 > x² + 2x + 1
  3. 33x² − 18x + 15 > 0, so x² − 6x + 5 > 0
  4. 4(x − 1)(x − 5) > 0: critical values 1 and 5
  5. 5x < 1 or x > 5

Answerx < 1, x > 5

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