Question

\[\frac{1}{x - 1} \leq 2\]

Answer 1

\[\frac{1}{x - 1} \leq 2\]
\[ \Rightarrow \frac{1}{x - 1} - 2 \leq 0\]
\[ \Rightarrow \frac{1 - 2x + 2}{x - 1} \leq 0\]
\[ \Rightarrow \frac{- 2x + 3}{x - 1} \leq 0\]
\[ \Rightarrow \frac{2x - 3}{x - 1} \geq 0\]

∴ \[x \in \left( - \infty , 1 \right) \cup [\frac{3}{2}, \infty )\]