Answer
$ (-2,9] $.
Work Step by Step
Step 1. For $\frac{3x-5}{x+2}-2\le0\Longrightarrow \frac{x-9}{x+2}\le0$, identify boundary points as $x=-2,9$.
Step 2. Form intervals $(-\infty,-2),(-2,9],[9,\infty)$.
Step 3. Choose test values for each interval $x=-3,0,10$.
Step 4. Test the inequality to get results: $False,\ True,\ False$
Step 5. We have the solution $ (-2,9] $.
