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

To solve the inequality \(-3(4k + 1) < 15\), we can follow these steps:

1. Distribute \(-3\) on the left side:
\[
-12k - 3 < 15
\]

2. Add \(3\) to both sides to isolate the term involving \(k\):
\[
-12k < 15 + 3
\]
\[
-12k < 18
\]

3. Divide both sides by \(-12\). Remember that dividing by a negative number reverses the inequality:
\[
k > \frac{18}{-12}
\]
\[
k > -\frac{3}{2}
\]

The solution set of the inequality is all values of \(k\) that are greater than \(-\frac{3}{2}\).

Any value greater than \(-1.5\) falls in this solution set. Some examples include \(0\), \(1\), \(2\), or specifically any number like \(-1\).

To summarize, any \(k\) value greater than \(-\frac{3}{2}\) satisfies the original inequality.