1. The problem statement, all variables and given/known data a and b are real numbers. Show l a-b l < l a l + l b l 2. Relevant equations Well, I know la+bl < lal + lbl by the triangle inequality. 3. The attempt at a solution If I can prove that la-bl < la+bl, then I'm done, but that most recent inequality almost seems too intuitive to write a formal proof. I can use the definition of absolute value to create cases perhaps, but I always get lost and seem to go nowhere Just to write the obvious stuff down. la-bl = a-b if a-b> 0 (or a>b) la-bl = b-a if a-b< 0 (or b>a) la+bl = a+b if a+b>0 (or a>-b) . la+bl = -a-b if a+b<0 ( or a<-b) I cant seem how to go somewhere with this.