Inequality with absolute values

1. May 7, 2014

DrunkenPhD

Wonder if this is true or just mistype:

|x+y| $\leq$ |x| +|y|

If this is true how to proof because cannot find it out anywhere written
Regards

2. May 7, 2014

Maylis

wouldn't it be easy to demonstrate this by putting in numbers?

3. May 7, 2014

pwsnafu

What have you tried?

4. May 7, 2014

micromass

Yes, please tell us what you tried.

Did you try plugging in some random numbers to check whether it works?
If it does always work, did you attempt a proof?

5. May 7, 2014

mathman

There are basically two cases - x and y same sign, x and y opposite sign. Work out each case.