Under what conditions is the identity |a-c| = |a-b| + |b-c| true? As the title suggests, I need to find out under what conditions the identity |a-c| = |a-b| + |b-c| is true.
I really have no clue as to where to start it. I know that I must know under what conditions the two sides of a triangle are equal to the remaining one. However, I really can't figure out when is that true. Would anyone care to enlighten me as to how would I go about doing this?

if $a<c \implies a<b<c$  and  if $c<a \implies c<b<a$ with those condition that identify is   always true. So for any b in the interval $(a,c)$ or $(c,a)$ the identity $|a-c| = |a-b| + |b-c|$   is true."
