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2000 AMC 12 Problem 5

Problem 5 of 25EasierAlgebra

If ∣x−2∣=p,|x - 2| = p, where x<2,x \lt 2, then what is x−p?x - p?

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Solution

Since x<2,x \lt 2, we have ∣x−2∣=2−x=p,|x - 2| = 2 - x = p, so x=2−p.x = 2 - p. Then x−p=(2−p)−p=2−2p. x - p = (2 - p) - p = 2 - 2p. Thus, the correct answer is C.

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Concepts: absolute value

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.