Answer: O S: {14}.
Explanation:
To solve this inequality, we can begin by isolating the term on the left side:
6(n - 5) < 3(n + 4)
6n - 30 < 3n + 12
Then, we can combine like terms on each side:
3n - 30 < 12
To solve for n, we can subtract 3n from both sides:
-30 < 12 - 3n
Then, we can add 30 to both sides:
0 < 12 - 3n + 30
This simplifies to:
0 < 42 - 3n
Finally, we can divide both sides by -3 to find the value of n:
0 > -14 - n
-14 < n
The solutions to the inequality are all the integers that are greater than -14. The given answer choices are 11, 14, 30, and 42. The only one of these that is greater than -14 is 14, so the correct answer is O S: {14}.