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

To solve the inequality \(-3(4k + 1) < 15\), let's first simplify it step by step.

1. Distribute \(-3\) across \((4k + 1)\):

\[
-12k - 3 < 15
\]

2. Next, we want to isolate \(k\). Start by adding \(3\) to both sides:

\[
-12k < 15 + 3
\]

\[
-12k < 18
\]

3. Now, divide both sides by \(-12\). Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign:

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

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

The solution set is \(k > -\frac{3}{2}\).

So, any value greater than \(-\frac{3}{2}\) (or \(-1.5\)) is in the solution set of the inequality.

For example, values like:
- \(0\)
- \(1\)
- \(-1\)
- \(-1.4\)

All of these values would fall within the solution set \(k > -\frac{3}{2}\).