Answer
$(-\infty,1)U(\frac{9}{5},\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{-4}{1-x}-5\lt0$ or $\frac{5x-9}{1-x}\lt0$
Step 2. Identify the boundary points as $x=1,\frac{9}{5}$
Step 3. Use test points at $x=0, \frac{3}{2},2$, the signs of the left side are $-, +, -$
Step 4. The inequality requires negative (outer regions), thus the solution intervals are $(-\infty,1)U(\frac{9}{5},\infty)$
