Problem:
For how many integer values of x is ∣2x∣≤7π ?
Answer Choices:
A. 16
B. 17
C. 19
D. 20
E. 21
Solution:
From 3<Ï€<3.142, it follows that
21=7â‹…3<7Ï€<7â‹…3.142=21.994<22
Because x is an integer, the values for 2x that make the inequality true are −20,−18,−16,…,−2, 0,2,…,18, and 20 . Each of these corresponds to a unique value of x. There are (E)21​ such values.
The problems on this page are the property of the MAA's American Mathematics Competitions