Quite often, $x_+$ indicates $\max\\{x,0\\}$ and $x_-$ indicates $-\min\\{x,0\\}=(-x)_+$. Under these conventions $$\lvert x\rvert=x_++x_-\\\ x=x_+-x_-$$
Quite often, $x_+$ indicates $\max\\{x,0\\}$ and $x_-$ indicates $-\min\\{x,0\\}=(-x)_+$. Under these conventions $$\lvert x\rvert=x_++x_-\\\ x=x_+-x_-$$