Can someone please explain this to me: Does |n+m|=|n| + |m| for all integers n and m? If so, give some examples. If not, give a counterexample.

Answer 1

Simply substitute numbers of opposing signs for n+m.

For example, n=-1, and m = 2

|n+m| = |-1+2| = |1| = 1
|n| + |m| = |-1| + |2| = 1+2=3