To solve the inequality \(-3(4k + 1) < 15\), we first need to distribute the \(-3\) on the left side:
\[ -12k - 3 < 15 \]
Next, we can isolate the term involving \(k\). First, add \(3\) to both sides of the inequality:
\[ -12k < 15 + 3 \]
\[ -12k < 18 \]
Now, divide both sides by \(-12\). Remember that dividing or multiplying both sides of an inequality by a negative number flips the inequality sign:
\[ k > \frac{18}{-12} \]
This simplifies to:
\[ k > -\frac{3}{2} \]
Thus, the solution set for the inequality is \(k > -1.5\).
Any value greater than \(-1.5\) will fall in the solution set. Examples of such values include \(0, 1, 2, -1, -0.5\), etc.