16Hit1600
Advanced MathVery hardCounting solutions of a two-term absolute-value equation

Advanced Math practice question

How many real solutions does the equation |x − 2| + |x − 6| = 4 have?

  1. A. Infinitely manyCorrect
  2. B. Two
  3. C. One
  4. D. None

Answer: A. Infinitely many

For every x between 2 and 6 inclusive, the two distances add to exactly 4.

Why the other answers are wrong

B. Two
Every point of the interval [2, 6] works, not just its ends.
C. One
Not just the midpoint.
D. None
x = 3, for instance, gives 1 + 3 = 4.

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