Without using a calculator, solve $x

Question

Without using a calculator, solve $x<\frac{3}{x-2}$.[3] Hence solve ${{\mathrm{e}}^{-x}}<\frac{3}{{{\mathrm{e}}^{-x}}-2}$.[2]

Accepted Answer

$x<-1$ or $2 < x < 3$; $-\ln 3 < x < -\ln 2$

2020 CJC Promo Q1