A basic inequality: $a-b\leq |a|+|b|$ Do we have the following inequality:
$$a-b\leq |a|+|b|$$
I have considered $4$ cases: 


*

*$a\leq0,b\leq0$

*$a\leq0,b>0$

*$a>0,b\leq0$

*$a>0,b>0$
and see this inequality is true. However I want to make sure about that.

Use the triangle inequality: 
$$
a - b \leq \vert a - b \vert \leq \vert a \vert + \vert b \vert.
$$
