To solve the inequality \(-3(4k + 1) < 15\), let's start by distributing the \(-3\):
\[ -12k - 3 < 15 \]
Next, add \(3\) to both sides:
\[ -12k < 18 \]
Now, divide both sides by \(-12\). Remember that dividing by a negative number reverses the inequality:
\[ k > -\frac{3}{2} \]
This means that the solution set includes all values greater than \(-\frac{3}{2}\).
Now let's evaluate the response options:
- \(-1\) is greater than \(-\frac{3}{2}\).
- \(-5\) is not, as it is less than \(-\frac{3}{2}\).
- \(-32\) is not, as it is also less than \(-\frac{3}{2}\).
- \(-4\) is not, as it is less than \(-\frac{3}{2}\).
Thus, the only value that falls within the solution set of the inequality is:
−1.