Question

$\frac{x}{x - 2} \leqslant 3$
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Answer 1

$\LARGE \bull \: \: \: \bf{Given :}$

$\to \large {\bold{ \sf \: \frac{x}{x - 2} \leqslant 3}}$

$\LARGE \bull \: \: \: \bf{ Solution :}$

$\sf \large \: \frac{x}{x - 2} \leqslant 3 \\ \\ \implies \sf \large \: {( \frac{x}{x - 2}) }^{ - 1} \geqslant {3}^{ - 1} \\ \\ \implies \sf \large1 - \frac{2}{x} \geqslant \frac{1}{3} \\ \\ \sf \implies \large \: \frac{2}{x} \leqslant \frac{2}{3} \\ \\ \implies \sf \large { \boxed{\boxed{ \sf x \geqslant 3}}}$

$\LARGE \sf \therefore\: x \in[3\:, \infty )$

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HOPE THIS IS HELPFUL...