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2022 YIJC Promo Q2

2022 YIJC Promo Q2

7 marks
Promo
  1. Using an algebraic method, solve the inequality \(2x-1\le \frac{5}{x-2}\).[3]
  2. Hence, solve
    1. \(2{{\mathrm{e}}^{x}}-1\le \frac{5}{{{\mathrm{e}}^{x}}-2}\),[2]
    2. \(2x+1\ge \frac{5}{x+2}\).[2]

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Answer:(a) \(x\le -\frac{1}{2}\) or \(2 < x\le 3\) (b)(i) \(\ln 2 < x\le \ln 3\) (ii) \(x\ge \frac{1}{2}\) or \(-3\le x<-2\)

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