Proving the Triangle Inequality in Real Analysis: abs(abs(x)-abs(y))<=abs(x-y)

[mb55113]

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?

 

[snipez90]

Well you've got half of it. The other inequality you need to demonstrate is |y| - |x| <= |x-y|. But what is an equivalent way of writing |x-y|?