Problem:
What is the value of x if ∣x−1∣=∣x−2∣?
Answer Choices:
A. −21​
B. 21​
C. 1
D. 23​
E. 2
Solution:
The equation implies that either
x−1=x−2 or x−1=−(x−2)
The first equation has no solution, and the solution to the second equation is x=(D)23​​.
OR
Since ∣x−a∣ is the distance of x from a,x must be equidistant from 1 and 2. Hence x=23​.
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions