Answer
$(-\infty,-\frac{3}{2})U[-\frac{13}{9},\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{x+2}{3+2x}-5\le0$ or $\frac{-9x-13}{3+2x}\le0$
Step 2. Identify the boundary point as $x=-\frac{3}{2},-\frac{13}{9}$
Step 3. Use test points at $x=-2, -\frac{53}{36}, 0$, the signs of the left side rational are $-,+,-$
Step 4. The inequality requires negative (outer regions, excluding $x=-\frac{3}{2}$), thus the solution intervals are $(-\infty,-\frac{3}{2})U[-\frac{13}{9},\infty)$