More precise way of solving inequality I need to solve this function:
$$
\lvert x^2-1\rvert\ge 2x-2\\
$$
I solved this equation:  
For $x<0$, the solution is non existing, here I got negative root, when I tried to solve quadratic function and for $x\ge 0$ I got points $x_1=-1$ and $x_2=3$.
My question is:
How do I set the solution of equation. Is there any procedure, with wich I can determine is equation valid for $[-1,3]$ or $[-\infty, -1]\lor [3, +\infty]$.
I know that I can just set the numbers and see the result, but I just want to now is there any other different way to do this.
Thanks.

Hints:
$$\begin{align*}|x|<1\implies x^2-1<0\implies |x^2-1|=1-x^2\\
|x|\ge 1\implies x^2-1\ge 0\implies |x^2-1|=x^2-1\end{align*}$$
So, for example, for  $\;x=-1\;$ you get
$$|(-1)^2-1|\ge 2(-1)-2\iff2\ge-4\;\color{green}{\checkmark}$$
