Question

What value falls in teh solution set of the inequality -3(4k + 1) < 15?

-4
-1
-5
-3/2

Answer 1

To solve the inequality \(-3(4k + 1) < 15\), we can start by distributing \(-3\):

\[
-12k - 3 < 15
\]

Next, we add \(3\) to both sides of the inequality:

\[
-12k < 15 + 3
\]
\[
-12k < 18
\]

Now, we divide both sides by \(-12\). Remember that when dividing by a negative number, we must reverse the inequality sign:

\[
k > \frac{18}{-12}
\]
\[
k > -\frac{3}{2}
\]

Now, we need to find which of the provided values falls within this solution set, \(k > -\frac{3}{2}\):

- \( -4 \) (not greater than \(-\frac{3}{2}\))
- \( -1 \) (greater than \(-\frac{3}{2}\))
- \( -5 \) (not greater than \(-\frac{3}{2}\))
- \( -\frac{3}{2} \) (not greater than \(-\frac{3}{2}\), since the inequality is strict)

The only value that satisfies the inequality \(k > -\frac{3}{2}\) is:

\(-1\)

Thus, the value that falls in the solution set of the inequality is \(-1\).