Question

Solve the following inequality:
$|x-2|⩽2x^2-9x-9$

Answer 1

$|x-2|\le 2x^2-9x-9$

$x-2\ge 0:x\ge 2,|x-2|=x-2$

$x-2<0:x<2,|x-2|=-(x-2)$

$-(x-2)\le 2x^2-9x-9:x\le \frac{4-\sqrt{38}}{2}orx\ge \frac{4+\sqrt{38}}{2}$

$x-2\le 2x^2-9x-9:x\le \frac{5-\sqrt{39}}{2}orx\ge \frac{5+\sqrt{39}}{2}$

$x\le \frac{4-\sqrt{38}}{2}orx\ge \frac{5+\sqrt{39}}{2}$