Çözüldü Sequences and First-Degree Inequalities

How many terms of the sequence (a_n) = ( 4n / (n + 6) ) are in the interval (1, 3)?

A) 11
B) 12
C) 13
D) 14
E) 15

1 < 4n / (n + 6) < 3 ⇒ n + 6 < 4n < 3(n + 6)
⇒ n + 6 < 4n ∧ 4n < 3(n + 6)
⇒ 2 < n ∧ n < 18
⇒ 2 < n < 18
n ∈ (2, 18)
18 - 2 - 1 = 15.

Source: Esen Publications, Question Bank with Subject Summaries, 11th Grade, Advanced Level, January 2016, Page 287, Example 6