# Proving inequalities

1. Nov 3, 2008

### Fairy111

1. The problem statement, all variables and given/known data
For real numbers x and y prove the following:

llxl - lyll < (or equal to) lx - yl

2. Relevant equations

3. The attempt at a solution

Im not really sure where to start, i was considering cases where x < 0 and say y< 0 and what that would imply say x-y would be. But im not sure how to continue.

2. Nov 3, 2008

### gabbagabbahey

Hint: What is $(|x|-|y|)^2$?...How about $(|x-y|)^2$?

3. Nov 3, 2008

You may need to consider a couple cases. There may be a little trick to doing this one.
I would say look at | x | equals and then look at what | y | equals.
So maybe add an subtract some thing to x, do the same for y. Then the triangle inequality says that
| a + b | <= |a| + |b| . This should be helpful in solving this. Does that help?

4. Nov 3, 2008

### Fairy111

ok, thankyou - i will have ago, althought im not very good at proving things! Also what does the double modulus sign mean?

5. Nov 3, 2008