Question

Evelyn is thinking of a number, n, and she wants her sister to guess the number. Her first clue is that one less than two times her number is between five and fifteen. Which compound inequality represents the range of numbers that Evelyn might be thinking of?

A) 5 < 2n - 1 < 15
B) 5 ≤ 2n - 1 ≤ 15
C) 5 ≤ 2n - 1 < 15
D) 5 ≤ 2n - 1 < 15

Answer 1

The correct compound inequality that represents the range of numbers that Evelyn might be thinking of is 5 < 2n - 1 < 15. By adding 1 and then dividing by 2, the inequality simplifies to 3 < n < 8.

Step-by-step explanation:

Evelyn's clue about her number, n, states that "one less than two times her number is between five and fifteen." This can be mathematically expressed as 5≤2n−1<15. The inequality 2n−1 represents "one less than two times her number," and it should fall within the range of values between five (inclusive) and fifteen (exclusive).

In this compound inequality, 5≤2n−1<15, the lower boundary 5≤2n−1 signifies that the expression 2n−1 is greater than or equal to 5, and the upper boundary 2n−1<15 indicates that 2n−1 is less than 15. This inequality range encapsulates the possible values for n that fulfill Evelyn's clue. Therefore, option C, 5≤2n−1<15, correctly represents the potential range of numbers that Evelyn might be thinking of.