Question

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

Answer 1

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

$\Rightarrow \frac{3(x-2)}{5}-\frac{5(2-x)}{3}\le 0$

$\Rightarrow \frac{3x-6}{5}-\frac{10-5x}{3}\le 0$

$\Rightarrow \frac{9x-18-50+25x}{15}\le 0$

$\Rightarrow 34x-68\le 0$

$\Rightarrow 17(x-4)\le 0$

$\Rightarrow x-4\le 0$

$\Rightarrow x\le 4$

$\therefore x\in (-\infty ,4]$