Question

Solve the following inequality:
$\frac{1-{\log }_{0.5}(-x)}{\sqrt{2-6x}}<0$

Answer 1

$x\ne 1/3$ and $x<0$

$lo{g}_{0.5}(-x)>1⟹-x>0.5⟹x<-0.5$

$⟹x\in (-\infty ,-0.5)$