Question

Solve the given inequality for real $x: \frac{3(x - 2)}{5} ≤ \frac{5(2 - x)}{3}$.

Answer 1

$\frac{3(x - 2)}{5} ≤ \frac{5(2 - x)}{3}$
⇒ 9(x-2) ≤ 25(2 - x)
⇒ 9x - 18 ≤ 50 - 25x
⇒ 9x - 18 + 25x ≤ 50
⇒ 34x - 18 ≤ 50
⇒ 34x ≤ 50+18
⇒34x ≤ 68
$⇒ \frac{34x}{34} ≤ \frac{68}{34}$
⇒ x ≤ 2
Thus, all real numbers x, which are less than or equal to 2, are the solutions of the given inequality.
Hence, the solution set of the given inequality is (–∞, 2].