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2024 AMC 12B Problem 3

Problem 3 of 25EasierAlgebraCounting & Probability

For how many integer values of xx is ∣2x∣≤7π?|2x| \le 7\pi?

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Solution

The inequality ∣2x∣≤7π|2x| \le 7\pi is equivalent to ∣x∣≤7π2≈10.99.|x| \le \dfrac{7\pi}{2} \approx 10.99. The integers satisfying this run from −10-10 to 10,10, which is 10+10+1=2110 + 10 + 1 = 21 values. Thus, the correct answer is E.

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Concepts: absolute value · counting integers in a range · estimation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.