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A-LevelMathematicsAlgebra9709/22 · Oct/Nov 2025 · Q37 Marks

Solve the inequality | 3x-4|<|2x+5|.

  1. (a)Solve the inequality | 3x-4|<|2x+5|. [4]
  2. (b)Hence find the largest integer N satisfying the inequality | 3×7⁰⁰¹ⁿ-4|<|2×7⁰⁰¹ⁿ +5|. [3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

  1. [4] (a) Solve 3x-4=2x+5 to obtain x=9
  2. [4] (a) Attempt solution of linear equation where 3x and 2x have different signs
  3. [4] (a) Obtain x = - 1 5
  4. [4] (a) Conclude - 1 5 ≤x≤9
  5. [3] (b) State 7⁰.⁰¹ⁿ = 9
  6. [3] (b) Use logarithms to find value of N
  7. [3] (b) Conclude with single integer 112

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2025 Paper 2 Variant 2, question 3.

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