Absolute Value Equality

1. Oct 19, 2013

lepton123

1. The problem statement, all variables and given/known data
abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement

2. Relevant equations

Triangle inequality?

3. The attempt at a solution
I have nothing :/

2. Oct 19, 2013

UltrafastPED

What is the absolute value of x? if x => 0 then abs(x)=x, else it is -x.

So make a table with all of the possible cases and see what happens!

3. Oct 19, 2013

lepton123

Drat, I was hoping that that I wouldn't have to do a case analysis; is there a more elegant way of solving this though?

4. Oct 19, 2013

UltrafastPED

I don't know elegant ... I grew up on a farm!

So once you have carried out the detailed work you can apply your own standards of elegance and cleverness ... and write something elegant!

5. Oct 19, 2013

verty

Assume (by renaming of variables) that x ≤ y ≤ z. Then you have 4 cases to check, it shouldn't be too tedious.

6. Oct 19, 2013

JanEnClaesen

x + y + z <= |x| + |y| + |z|
- x - y - z <= |x| + |y| + |z|

(definition of the absolute value)