Verifying the triangle inequality I am going through some practice problems in Abbott's Analysis text, and one of them is the following: Verify the triangle inequality in the special case where 
a) a and b have the same sign; 
b) $a \geq 0$, $b < 0$, and $a+b \geq 0$.
I do not know where to begin because I don't know how exactly to go about the 'verification' given such conditions. Thanks!

For instance, in case (a), you could distinguish between two possibilities:


*

*$a,b \geq 0$. Then $a+b \geq 0 $ too and $\mid a+b\mid = a+b$ which is certainly equal to $\mid a \mid +\mid b\mid = a +b$.

*$a,b \leq 0$. Then $a+b \leq 0$ too and $\mid a+b\mid = -(a+b)$ which is certainly equal to $\mid a \mid +\mid b\mid = -a -b$.

