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To solve the inequality \(-3(4k + 1) < 15\), let's first simplify it step by step.
1. Distribute \(-3\) across \((4k + 1)\):
\[
-12k - 3 < 15
\]
2. Next, we want to isolate \(k\). Start by adding \(3\) to both sides:
\[
-12k < 15 + 3
\]
\[
-12k < 18
\]
3. Now, divide both sides by \(-12\). Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign:
\[
k > \frac{18}{-12}
\]
\[
k > -\frac{3}{2}
\]
The solution set is \(k > -\frac{3}{2}\).
So, any value greater than \(-\frac{3}{2}\) (or \(-1.5\)) is in the solution set of the inequality.
For example, values like:
- \(0\)
- \(1\)
- \(-1\)
- \(-1.4\)
All of these values would fall within the solution set \(k > -\frac{3}{2}\).