Hi guys, I'm doing a case by case proof of

$\displaystyle |a+b| \leq |a|+|b|$

from Spivak, and he says:

When $\displaystyle a \geq 0$ and $\displaystyle b \leq 0$, we must prove that:

$\displaystyle |a+b| \leq a-b$

I'm a bit stuck on his line of reasoning, could someone explain why we have to prove the above?