Question

what value falls in the solution set of the inequality -3(4k + 1) 15

Answer 1

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.