Why is $ F_{|x|}(x) \equiv F_{x}(x)-F_{x}(-x) $?

Question

I don't fully understand the jump from

$\quad F_{|X|}(x)= Pr[-x \leq X \leq x]$

to

$\quad F_{|x|}(x) \equiv F_{x}(x)-F_{x}(-x) \quad$

maybe someone can give an intuitive explanation.

Answer 1

Since $F(x)=P(X\leq x )$ we have that $$P(-x\leq X\leq x)=F(x)-F(-x)$$