# How do you solve the inequality abs(2x - 5) ≤ 3x?

May 25, 2016

$x \ge 1$.

#### Explanation:

As $| 2 x - 5 | \ge 0 , 3 x \ge 0$. So, $x \ge 0$.

The inequality $| 2 x - 5 | \le 3 x$ is the combined inequality for

$2 x - 5 \le 3 x \mathmr{and} - \left(2 x - 5\right) \le 3 x$,

So, $x \ge - 5 \mathmr{and} x \ge 1$.

Negative x is inadmissible . So, $x \ge 1$.