To solve the inequality \(-3(4k + 1) < 15\), we first distribute the \(-3\) on the left side:
\[ -3 \cdot 4k - 3 \cdot 1 < 15 \]
This gives us:
\[ -12k - 3 < 15 \]
Next, we add \(3\) to both sides to isolate the term with \(k\):
\[ -12k < 15 + 3 \] \[ -12k < 18 \]
Now, we divide both sides by \(-12\). Remember to flip the inequality sign when dividing by a negative number:
\[ k > \frac{18}{-12} \]
Simplifying \(\frac{18}{-12}\):
\[ k > -\frac{3}{2} \]
Now we can identify the values that fall in the solution set of \(k > -\frac{3}{2}\).
Among the provided options:
- \(-4\) (is not greater than \(-\frac{3}{2}\))
- \(-5\) (is not greater than \(-\frac{3}{2}\))
- \(-32\) (is not greater than \(-\frac{3}{2}\))
- \(-1\) (is greater than \(-\frac{3}{2}\))
Thus, the value that falls in the solution set of the inequality \(-3(4k+1)<15\) is:
\(-1\)