1. The problem statement, all variables and given/known data Verify the rule that for two real numbers X and Y then |X+Y|≤|X|+|Y| 2. Relevant equations 3. The attempt at a solution 1. When all the variables are positive: |X+Y|=(X+Y) because (X+Y)>0 |X|=X because X>0 |Y|=Y because Y>0 So we got (X+Y)=X+Y 2. When all the variables are negative: |-X+(-Y)|= -(-[X+Y])= (X+Y) because -(X+Y)<0 |-X|= -(-X)=X because -X<0 |-Y|= -(-Y)=Y because -Y<0 Now we got (X+Y)=X+Y 3. When the two variables have opposite signs: |X+(-Y)|= (X-Y) because (X-Y)>0 |X|=X because X>0 |-Y|= -(-Y)=Y because Y<0 Finally we got: (X-Y)< X+Y ================================================== So that solution was shot down as a bit shaky. How about the one below then? |X+Y|≤|X|+|Y| |X+Y|-|X|-|Y|≤0 If we remove the variables from the modulus we get X+Y-X-Y≤0 Thanks.