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AMC 10B/12B 2024 (Problem 3/3)

For how many integer values of

x

is

|2x|\le7\pi

?

\text{(A)}\;16

\text{(B)}\;17

\text{(C)}\;19

\text{(D)}\;20

\text{(E)}\;21

Core

Absolute Value

Major

Approximations and Bounds

Your answer:

ABCDE

|2x|\le7\pi

Since

2x

is an integer and

7\pi

is irrational,

-7\pi<2x<7\pi

Since

\pi<3.142

,

-7(3.142)<2x<7(3.142)

-21.994<2x<21.994

Since

2x

is an even integer,

-20\le2x\le20

-10\le x\le10

Therefore, the number of integer values of

x

is

10-(-10)+1=21

(E)

21

AMC 10B/12B 2024 (Problem 14/9)
AMC 10B/12B 2023 (Problems 9/13)

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