For how many integer values of x is |2x| ≤ 7π?

2024 AMC 10B Problem 3

Attempt Problem 3 of the 2024 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 10B solutions, or check the answer key.

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For how many integer values of

x

|2x| \le 7\pi?

16

17

19

20

21

Divide by

2

: the inequality is

|x| \le 3.5\pi

3.5\pi \approx 10.99,

x

ranges over the integers with

|x| \le 10

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.