2024 AMC 12B 第 3 题

Rewrite as $|x| \le \dfrac{7\pi}{2}$ and estimate $\dfrac{7\pi}{2}$ as a decimal

Since $\dfrac{7\pi}{2} \approx 10.99,$ count the integers from $-10$ to $10$

The inequality $|2x| \le 7\pi$ is equivalent to $|x| \le \dfrac{7\pi}{2} \approx 10.99.$ The integers satisfying this run from $-10$ to $10,$ which is $10 + 10 + 1 = 21$ values.

Thus, the correct answer is E.