How to prove $x^2<4 \implies|x|<2$? 
How to prove $x^2<4 \implies|x|<2$?

I don't know exactly there is a proof for this or we take this as an axiom. Please help.
What I did so far is, $$x^2-4<0$$
$$(x-2)(x+2)<0$$
$$-2<x<2$$
From this step can we directly say? $|x|<2$


What I did so far is, $$x^2-4<0$$
  $$(x-2)(x+2)<0$$

Since $\,x^2=|x|^2\,$, you could also factor it as:
$$\left(|x|-2\right)\left(|x|+2\right) \lt 0$$
Given that $\,|x|+2 \gt 0\,$ it follows that $\,|x| - 2\lt 0\,$.
