(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Another Absolute Value Proof

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