Question

Determine which integer makes the inequality 6(n - 5) < 3(n + 4) true.

O S: {11}
O S:{14}
› S:{30}
D S:{42}

Answer 1

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}.