Is the Inequality with Absolute Values |x+y| ≤ |x| + |y| True?

[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

 

[gfd43tg]

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

 

[pwsnafu]

If this is true how to proof
Regards

What have you tried?

 

[micromass]

What have you tried?

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?

 

[mathman]

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

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