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## Homework Statement

Prove: abs(abs(x)-abs(y))<=abs(x-y)

## Homework Equations

Triangle Inequality:

abs(a+b)<=abs(a)+abs(b)

## 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?