Absolutely lazy mistake

Algebra Level 3

Jook believes that since Math is beautiful, it must always work out. This leads him to think that

$| a-c | = | a - b | + | b - c |,$

with the reasoning that " $-b$ and $+b$ will cancel out". How many ordered sets of integers $(a, b, c)$ , each of which are between 0 and 10 (inclusive), satisfy

$| a-c | = | a - b | + | b - c |?$