Answer
$(-\infty,-\frac{3}{2})U[-\frac{1}{2},\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{10}{3+2x}-5\le0$ or $\frac{-5-10x}{3+2x}\le0$
Step 2. Identify the boundary points as $x=-\frac{3}{2},-\frac{1}{2}$
Step 3. Use test points at $x=-2, -1, 0$, the signs of the left side are $-, +, -$
Step 4. The inequality requires negative (outer regions, excluding $x=-\frac{3}{2}$), thus the solution intervals are $(-\infty,-\frac{3}{2})U[-\frac{1}{2},\infty)$
