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.

$$|-x-y| \leq |x| + |y|\\
|-1(x+y)| \leq |x| + |y|\\
|x+y||-1|\leq |x| + |y|\\
1|x+y|\leq |x| + |y|\\
|x+y|\leq |x| + |y|
$$
I think that you can take it from here as long as you use the fact that $|x| = \max(x, -x)$
