Question

Solve the following inequality:
$\left|\frac{2}{x-4}\right|>1$

Answer 1

$\left|\frac{2}{x-4}\right|>1$

$-1>\left|\frac{2}{x-4}\right|>1$

$\left(i\right)\frac{2}{x-4}>1$

$\frac{2}{x-4}-1>0$

$\frac{2-x+4}{x-4}>0$

$\frac{6-x}{x-4}>0$

$\frac{x-6}{x-4}<0$

$x\epsilon (4,6)$

$\left(ii\right)\frac{2}{x-4}+1<0$

$\frac{2+x-4}{x-4}<0$

$\frac{x-2}{x-4}<0$

$x\epsilon (2,4)$

$x\epsilon (2,6)$