Question

(3x - 5)/(2 - x) >= 2

Answer 1

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$\displaystyle \bf \frac{3x-5}{2-x} \geq 2 \\\\\\\frac{3x-5}{2-x} -2\geq 2-2\\\\\\\frac{3x-5}{2-x} -2\geq 0\\\\\\\frac{-2\left(2-x\right)+3x-5}{2-x}\geq 0\\\\\\\frac{-2\cdot 2 - (-2\cdot x)+3x-5}{2-x}\geq 0 \\\\\\\frac{-4 +2x+3x-5}{2-x}\geq 0\\\\\\\frac{5x-9}{2-x}\geq 0\\\\\\ \frac{9}{5}\le \:x < 2$

$\boxed{\displaystyle \bf x \in \Big[\ \frac{9}{5} \ ; \ 2\Big) }$