Question

What value falls in the solution set of the inequality −3(4k+1)<15?(1 point)%0D%0AResponses%0D%0A%0D%0A−1%0D%0Anegative 1%0D%0A%0D%0A−5%0D%0Anegative 5%0D%0A%0D%0A−32%0D%0AStart Fraction negative 3 over 2 End Fraction%0D%0A%0D%0A−4

Answer 1

To solve the inequality \(-3(4k + 1) < 15\), we will first distribute the \(-3\):

\[
-12k - 3 < 15
\]

Next, we will add \(3\) to both sides:

\[
-12k < 18
\]

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

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

Now, we need to find which values fall within this solution set \(k > -\frac{3}{2}\). The provided options are:

- \(-1\)
- \(-5\)
- \(-32\)
- \(-\frac{3}{2}\)
- \(-4\)

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

\(-1\)

Thus, the correct response is:

**−1**