# Math Help - Prove || x|-|y|| ≤ |x-y|

1. ## Prove || x|-|y|| ≤ |x-y|

Prove || x|-|y|| ≤ |x-y|, ∀x, y ∈ R

2. Hint: Use the triangle inequality and the fact that for all $x,y$, $|x| = |x + (y-y)| = |(x-y) + y|$.