Question

Solve the inequality for real $x$.

$\frac{3(x-2)}{5}\le \frac{5(2-x)}{3}$

Answer 1

Given, $\frac{3(x-2)}{5}\le \frac{5(2-x)}{3}$
$\Rightarrow 9(x-2)\le 25(2-x)$
$\Rightarrow 9x-18\le 25(2-x)$
$\Rightarrow 9x-18+25x\le 50$
$\Rightarrow 34x-18\le 50$
$\Rightarrow 34x\le 50+18$
$\Rightarrow 34x\le 68\Rightarrow x\le 2\text{or}x\in (-\infty ,2]$