Question

Solve the following inequalities
$x^2-|x|-2⩾0.$

Answer 1

$x^2-|x|-2\ge 0$

Let $|x|$ be $t$.

$t\ge 0$

$t^2-t-2\ge 0$

$(t-2)(t+1)\ge 0$

$tϵ(-\infty ,-1)\cup (2,\infty )$

As $t\ge 0$

$t\in (2,\infty )$

$|x|\in (2,\infty )$

$x\in (-\infty ,-2)\cup (2,\infty )$