1. The problem statement, all variables and given/known data Prove: abs(abs(x)-abs(y))<=abs(x-y) 2. Relevant equations Triangle Inequality: abs(a+b)<=abs(a)+abs(b) 3. The attempt at a solution This is what i have so far: Let a=x-y and b=y. Then abs(x-y+y) <= abs(x-y)+abs(y) which becomes abs(x)-abs(y)<=abs(x-y). From here i get stuck can anybody help me?