Using Triangle Inequality to find a magnitude

[TeenieBopper]

Homework Statement

Let a, x, and y be real numbers and let E > 0. Suppose that |x-a|< E and |y-a|< E. Use the Triangle Inequality to find an estimate for the magnitude |x-y|.

Homework Equations

The Triangle Inequality states that |a+b| <= |a| + |b| is valid for all real numbers a and b.

The Attempt at a Solution

|x-a| = |x-y+y-a| <= |x-y| + |y-a|

I'm fairly certain this conversion/inequality is important because it contains three of the four elements from the problem ( |x-a|, |y-a|, and |x-y|). However, I am stuck on how to get E involved and determine an estimate for |x-y|.

 

[lanedance]

you want to try and get |x-y| on the left of the <= sign

now its a little confusing as you used "a" in the tri eq as well (good notation always helps avoid confusion), so let's re-write it
|c+b| <= |c|+ |b|

then how about letting
c=x-a
n=a-y