1. The problem statement, all variables and given/known data If a and b have opposite signs then |a + b| < |a| + |b| 2. Relevant equations No equations. 3. The attempt at a solution Well first start with "a" positive and "-b" negative. We have : |a|=a |-b|=b |a-b|=a-b We begin with 0 < |a| + |-b| Then : 0 < |a| + |-b| -a a < |a| + |-b| a + (-b) < |a| + |-b| which gives us : |a-b| < |a| + |-b| We see that the result stays the same when we have -a and b. |-a|=a |b|=b |b-a|=b-a We begin with 0 < |b| + |-a| Then : 0 < |b| + |-a| -b b < |b| + |-a| b + (-a) < |b| + |-a| which gives us : |b-a| < |b| + |-a| Thus wee see that when the signs are different the following inequality holds : |a + b| < |a| + |b| Is it any good ?