Absolutely lazy mistake

Algebra Level 3

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

ac=ab+bc, | a-c | = | a - b | + | b - c |,

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

ac=ab+bc? | a-c | = | a - b | + | b - c |?

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