Question

Solve the following inequality:
$\sqrt{2x-1}<x-2.$

Answer 1

$2x-1\ge 0$

$xϵ[\frac{1}{2},\infty )$

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

Squarring both sides

$2x-1<x^2-4x+4$

$x^2-6x+5>0$

$(x-5)(x-1)>0$

$xϵ(-\infty ,1)\cup (5,\infty )$

$xϵ[\frac{1}{2},1)\cup (5,\infty )$