Using an algebraic method, solve the inequality ${x - 3 [3] Hence, solve ${e^{2x} - 3 [2] ${x + 3 > \frac{8}{x + 1}}$. [2]

2023 MI PRU2 P1 Q3

7 marks

Promo

Using an algebraic method, solve the inequality ${x - 3 < \frac{8}{x - 1}}$.[3]
Hence, solve
1. ${e^{2x} - 3 < \frac{8}{e^{2x} - 1}}$,[2]
2. ${x + 3 > \frac{8}{x + 1}}$.[2]

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Answer:(a) $x<-1$ or $1<x<5$ (b)(i) $0<x<\ln\sqrt5$ (b)(ii) $-5<x<-1$ or $x>1$

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