For any two integers x and y, |x+y| = |x|+|y|

Question

Im doing a counterexample & conjectures homework,  this is tje only one I need to solve and I don't know if it's true. 

Thanks 

Djcriss

Answer 1

It is false. Take x = 1 and y = -1.

Answer 2

Dj,

 

Are you familiar with the "triangle" inequality?  It is always true that 

 

|x + y| ≤ |x| + |y|.

 

If both numbers are positive or both numbers are negative, then

 

|x + y| = |x| + |y|.