Question

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

−5
negative 5

−4
negative 4

−3/2
Start Fraction negative 3 over 2 End Fraction

−1

Answer 1

To solve the inequality \(-3(4k + 1) < 15\), we can start by distributing the \(-3\):

\[
-12k - 3 < 15
\]

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

\[
-12k < 18
\]

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

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

Now, we determine which values fall into the solution set \(k > -\frac{3}{2}\).

Among the given options:

1. \(-5\) (Not greater than \(-\frac{3}{2}\))
2. \(-4\) (Not greater than \(-\frac{3}{2}\))
3. \(-\frac{3}{2}\) (Not greater than \(-\frac{3}{2}\))
4. \(-1\) (Greater than \(-\frac{3}{2}\))

The value that falls in the solution set of the inequality is:

\(-1\)