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2021 AMC 12B Problem 1

Problem 1 of 25EasierAlgebra

How many integer values of xx satisfy ∣x∣<3π?|x| \lt 3\pi?

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Solution

Since 3π≈9.42,3\pi \approx 9.42, the inequality ∣x∣<3π|x| \lt 3\pi means −9.42<x<9.42.-9.42 \lt x \lt 9.42. The integers in this range run from −9-9 to 9,9, giving 1919 values. Thus, the correct answer is D.

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Concepts: absolute value · estimation

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