Answer
$(-\infty,\frac{2}{3}]U(\frac{5}{3},\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{-6}{3x-5}-2\le0$ or $\frac{4-6x}{3x-5}\le0$
Step 2. Identify the boundary points as $x=\frac{2}{3},\frac{5}{3}$
Step 3. Use test points at $x=0, 1,2$, the signs of the left side are $-, +, -$
Step 4. The inequality requires negative (outer regions, excluding $x=\frac{5}{3}$), thus the solution intervals are $(-\infty,\frac{2}{3}]U(\frac{5}{3},\infty)$
