Answer
$(-\infty,-\frac{2}{3})U[-\frac{1}{2},0)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{-5}{3x+2}-\frac{5}{x}\ge0$ or $\frac{-20x-10}{x(3x+2)}\ge0$
Step 2. Identify the boundary point as $x=-\frac{2}{3},-\frac{1}{2},0,$
Step 3. Use test points at $x=-1, -\frac{7}{12},-\frac{1}{4},1$, the signs of the left side rational are $+, -,+,-$
Step 4. The inequality requires positive (1st and 3rd regions, excluding $x=-\frac{2}{3},0, $), thus the solution intervals are $(-\infty,-\frac{2}{3})U[-\frac{1}{2},0)$
