2004 AMC 10A Problem 4

What is the value of

x

|x - 1| = |x - 2|?

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Solution

Since

|x - 1|

and

|x - 2|

are the distances from

x

1

and

2,

the point

x

is equidistant from

1

and

2.

That midpoint is

x = \dfrac{1 + 2}{2} = \dfrac{3}{2}.

Thus, the correct answer is D.

Concepts: absolute value · midpoint

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