Answer
$(-\infty,1)U(2,\infty)$. See graph.
Work Step by Step
Step 1. $\frac{2x-6}{1-x}\lt2 \longrightarrow \frac{2x-6}{1-x}-2\lt0 \longrightarrow \frac{4x-8}{1-x}\lt0$
Step 2. Identify boundary points $x=1,2$ and intervals $(-\infty,1),(1,2),(2,\infty)$
Step 3. Choose test values $x=0,1.5,3$ for each interval and evaluate the inequality to get $True,\ False,\ True$
Step 4. Thus we have the solution interval(s) $(-\infty,1)U(2,\infty)$. See graph.