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

2024 AMC 10B Problem 3 — Solution

2024 AMC 10B Problem 3

Below is the professionally curated solution for Problem 3 of the 2024 AMC 10B, 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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Concepts:absolute value estimation counting integers in a range

Difficulty rating: 1050

For how many integer values of $x$ is $|2x| \le 7\pi?$

$16$

$17$

$19$

$20$

$21$

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.

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