Problem: If ∣x−2∣=p|x-2|=p∣x−2∣=p, where x<2x<2x<2, then x−p=x-p=x−p=
Answer Choices:
A. −2-2−2 B. 222 C. 2−2p2-2 p2−2p D. 2p−22 p-22p−2 E. ∣2p−2∣|2 p-2|∣2p−2∣
Solution:
Since x<2x<2x<2, it follows that ∣x−2∣=2−x|x-2|=2-x∣x−2∣=2−x. If 2−x=p2-x=p2−x=p, then x=2−px=2-px=2−p. Thus x−p=2−2px-p=2-2 px−p=2−2p.
Answer: C\boxed{C}C.
The problems on this page are the property of the MAA's American Mathematics Competitions