1. The problem statement, all variables and given/known data Hi guys, I would just like someone to go over my method for this derivation/proof ( not sure of the right word to use here). Anyway I think this is right method, but just feel like I am missing something. Could someone please check my method. Thanks in advance. 2. Relevant equations $$|x|= x\geq 0 , -x < 0 $$ $$|a-b|\leq|a|-|b|$$ 3. The attempt at a solution By using the formal definition of the absolute value I get this: 1.$$-|a|\leq a\leq |a|$$ 2.$$-|b|\leq b\leq |b|$$ 1-2: $$-(|a|-|b|)\leq a-b \leq |a|-|b| $$ Therefore I get: $$|a-b|\leq|a|-|b|$$ Is this correct? Is there any improvements that anyone could share. I do have a couple more variations of the triangle inequality to go through but want to try the first before posting.