@cricketfan1997
I use the words proof/show loosely. I still consider a show a proof, but yes in a proof question i would not do a 'show' (if that made any sense LOL).
The full question says to consider the cases (a>0,b>0),(a>0,b<0),(a<0,b<0),(a<0,b>0)
and show that a+b <= |a+b|
So basically if...