Question

Solve the following inequality:
$|x^2-2x|<x$

Answer 1

$|x^2-2x|<x$

$x^2-2x>-x$

$x^2-3x>0$

$x(x-1)>0$

$xϵ(-\infty ,0)\cup (1,\infty )$

and

$x^2-2x<x$

$x^2-3x<0$

$x(x-3)<0$

$xϵ(0,3)$

Therefore, $xϵ(1,3)$