Question

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

Answer 1

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

$-2<\frac{2x-1}{x-1}<2$

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

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

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

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

$x\epsilon (1,\infty )$

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

$\frac{2x-1+2x-2}{x-1}<0$

$\frac{4x-3}{x-1}<0$

$\frac{x-\frac{3}{4}}{x-1}<0$

$x\epsilon (1,\frac{3}{4})$

$x\epsilon (1,\infty )from\left(i\right)\&\left(ii\right)$