Question:
$\frac{1}{x-1} \leq 2$
Solution:
$\frac{1}{x-1} \leq 2$
$\Rightarrow \frac{1}{x-1}-2 \leq 0$
$\Rightarrow \frac{1-2 x+2}{x-1} \leq 0$
$\Rightarrow \frac{-2 x+3}{x-1} \leq 0$
$\Rightarrow \frac{2 x-3}{x-1} \geq 0$
$\therefore x \in(-\infty, 1) \cup\left[\frac{3}{2}, \infty\right)$
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