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A-LevelMathematicsAlgebra9709/21 · Oct/Nov 2019 · Q15 Marks

Solve the inequality |2x – 7| < |2x – 9|.

  1. (i)Solve the inequality |2x – 7| < |2x – 9|.[3]
  2. (ii)Hence find the largest integer n satisfying the inequality |2 ln n – 7| < |2 ln n − 9|.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [M1] State or imply non-modular inequality (2x−7)² < (2x−9)² or corresponding equation or linear equation (with signs of 2x different)
  2. [A1] Obtain critical value 4
  3. [A1] State x < 4 only
  4. [M1] Attempt to find n from Inn = their critical value from part (i)
  5. [A1] Obtain or imply n<e⁴ and hence 54

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 2 Variant 1, question 1.

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