Proof of absolute inequality I am new to proofs and would like some help understanding how to prove the following abs inequality.
$$| -x-y | \leq |x| + |y|.$$
I think I should take out the negative in the left absolute value function.? Then prove for the triangle inequailty.

We have $\mid -x-y\mid = \mid -(x+y) \mid = \mid x+y \mid \leq \mid x \mid + \mid y \mid$. For the least step we use the triangle inequality. Supposing you work in $\mathbb R$ look here for a proof: Proof of triangle inequality.
