If |x - 2| = p, where x < 2, then what is x - p?

2000 AMC 12 Problem 5

Attempt Problem 5 of the 2000 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2000 AMC 12 solutions, or check the answer key.

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|x - 2| = p,

where

x \lt 2,

then what is

x - p?

-2

2

2 - 2p

2p - 2

|2p - 2|

Since

x \lt 2,

the quantity

x - 2

is negative, so

|x - 2| = 2 - x

Solve

2 - x = p

for

x,

then compute

x - p

Since

x \lt 2,

we have

|x - 2| = 2 - x = p,

x = 2 - p.

Then

x - p = (2 - p) - p = 2 - 2p.

Thus, the correct answer is C.