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

\[ | a-c | = | a - b | + | b - c |? \]

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