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?
- A. Infinitely manyCorrect
- B. Two
- C. One
- 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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