2024 AMC 10B Problem 3

For how many integer values of

x

|2x| \le 7\pi?

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Solution

Divide by

2

to get

|x| \le 3.5\pi \approx 10.996.

The integers that fit run from

-10

up to

10,

and there are

21

of them. Thus, E is the correct answer.

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

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