Answer
$(-\infty,1)\cup(2,\infty)$.
See graph.
Work Step by Step
Step 1. $\frac{2x-6}{1-x}-2\lt0 \Longrightarrow \frac{4x-8}{1-x}\lt0$, identify boundary points $x=1,2$.
Step 2. Form intervals $(-\infty,1),(1,2),(2,\infty)$.
Step 3. Choose test values for each interval $x=0,1.5,3$.
Step 4. Test the inequality to get results $True,\ False,\ True$.
Step 5. Thus we have the solution $(-\infty,1)\cup(2,\infty)$.
Step 6. See graph.
