Answer
$(-2,-\frac{5}{3}]$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{1}{x+2}-3\ge0$ or $\frac{-3x-5}{x+2}\ge0$
Step 2. Identify the boundary points as $x=-2,-\frac{5}{3}$
Step 3. Use test points at $x=-3, -\frac{3}{2}, 0$, the signs of the left side are $-, +, -$
Step 4. The inequality requires positive (middle regions, excluding $x=-2$), thus the solution intervals are $(-2,-\frac{5}{3}]$