Question

What value falls in the solution set of the inequality −3(4k+1)<15?(1 point)
Responses

−4
negative 4

−32
Start Fraction negative 3 over 2 End Fraction

−1
negative 1

−5

Answer 1

To solve the inequality \(-3(4k + 1) < 15\), we first distribute \(-3\) on the left side:

\[
-12k - 3 < 15
\]

Next, we add \(3\) to both sides:

\[
-12k < 18
\]

Now, we divide both sides by \(-12\). Remember that when we divide by a negative number, we must reverse the inequality sign:

\[
k > -\frac{3}{2}
\]

This means that \(k\) can be any value greater than \(-\frac{3}{2}\).

Now let's evaluate the responses to see which values satisfy \(k > -\frac{3}{2}\).

1. \(-4\) (is not greater than \(-1.5\))
2. \(-32\) (is not greater than \(-1.5\))
3. \(-1\) (is greater than \(-1.5\))
4. \(-5\) (is not greater than \(-1.5\))

From this, the only value in the solution set is:

\(-1\)

So, the answer is \(-1\).