To solve the inequality \( -3(4k + 1) < 15 \), let's solve it step by step:
1. Distribute the -3:
\[
-12k - 3 < 15
\]
2. Add 3 to both sides:
\[
-12k < 15 + 3
\]
\[
-12k < 18
\]
3. Divide both sides by -12 (remember to flip the inequality when dividing by a negative number):
\[
k > \frac{18}{-12}
\]
\[
k > -\frac{3}{2}
\]
Thus, the solution to the inequality is \( k > -\frac{3}{2} \).
Now, we need to find which of the provided values falls in the solution set \( k > -\frac{3}{2} \):
- **−1**: This is greater than \(-\frac{3}{2}\) (approximately \(-1.5\)), so it satisfies the inequality.
- **−3/2**: This is equal to \(-\frac{3}{2}\), thus does not satisfy \( k > -\frac{3}{2} \).
- **−5**: This is less than \(-\frac{3}{2}\), so it does not satisfy the inequality.
- **−4**: This is also less than \(-\frac{3}{2}\) and does not satisfy the inequality.
Therefore, the value that falls in the solution set of the inequality \( -3(4k + 1) < 15 \) is:
**−1**.