Answer
$(-\infty,2)U[5,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{3}{x-2}-1\lt0$ or $\frac{5-x}{x-2}\lt0$
Step 2. Identify the boundary points as $x=2,5$
Step 3. Use test points at $x=0, 3,6$, the signs of the left side are $-, +, -$
Step 4. The inequality requires negative (outer regions excluding $x=2$), thus the solution intervals are $(-\infty,2)U[5,\infty)$