Answer
$(-2,9]$
Work Step by Step
Step 1. Rewrite the inequality $\frac{3x-5}{x+2}-2\le0$ as $\frac{x-9}{x+2}\le0$. Identify boundary points (zeros and asymptotes) as $x=-2,9$ which divide the x-axis into three intervals $(-\infty,-2),(-2,9],[9,\infty)$
Step 2. Choose test values in each interval $x=-3,0,10$ and test the inequality to get $ False,\ True,\ False$
Step 3. Thus the solution interval is $(-2,9]$
