Hello,

I had a question regarding triangle inequalities.

I proved the inequality abs(x+y) <= abs(x) + abs(y).

Second part of question is asking to use the triangle inequality to prove "shortest path" version:

for all x,y,z in R, abs(x-y) <= abs(x-z) + abs(z-x).

I've got no idea on how to start this part.

Should there be a y in the right half of the inequality? Am I supposed to assume something about y S.T it doesn't need to be

in the right half?

Thanks all