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Solve the fol...

Question

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

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Solution

$x \neq 1 / 3$ and $x < 0$
$l o g_{0.5} (- x) > 1 ⟹ - x > 0.5 ⟹ x < - 0.5$
$⟹ x \in (- \infty, - 0.5)$

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