2000 AMC 12 Problems/Problem 5

Problem

If $\displaystyle |x - 2| = p,$ where $\displaystyle x < 2,$ then $\displaystyle x - p =$

$\mathrm{(A) \ -2 } \qquad \mathrm{(B) \ 2 } \qquad \mathrm{(C) \ 2-2p } \qquad \mathrm{(D) \ 2p-2 } \qquad \mathrm{(E) \ |2p-2| }$

When $\displaystyle x < 2,$ , $x-2$ is negative.

So $\displaystyle x - 2 = -p,$ .

Therefore:

$x-2=-p$

$x=2-p$

$\displaystyle x-p = (2-p)-p = 2-2p \Rightarrow D$