Answer
$(-\infty,6)U[ \frac{15}{2},\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{3}{x-6}-2\le0$ or $\frac{15-2x}{x-6}\le0$
Step 2. Identify the boundary points as $x=6, \frac{15}{2}$
Step 3. Use test points at $x=0, 7, 8$, the signs of the left side are $-, +, -$
Step 4. The inequality requires negative (outer regions excluding $x=6$), thus the solution intervals are $(-\infty,6)U[ \frac{15}{2},\infty)$