Question

What value falls in the solution set of the inequality $-3(4k+1)\lt 15$ ? (1 point)
$-4$
$-1$
$\frac {-3}{2}$
$-5$

Answer 1

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

\[
-12k - 3 < 15
\]

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

\[
-12k < 15 + 3
\]

\[
-12k < 18
\]

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

\[
k > \frac{18}{-12}
\]

Simplifying \(\frac{18}{-12}\):

\[
\frac{18}{-12} = \frac{3}{-2} = -\frac{3}{2}
\]

Thus, the inequality becomes:

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

Now, we need to determine which values from the given options fall within the solution set \(k > -\frac{3}{2}\). The options are:

1. \(-4\)
2. \(-1\)
3. \(-\frac{3}{2}\)
4. \(-5\)

Let's check each option:

1. For \(k = -4\):
\(-4 > -\frac{3}{2}\) is **false** (since \(-4\) is less than \(-1.5\)).

2. For \(k = -1\):
\(-1 > -\frac{3}{2}\) is **true** (since \(-1\) is greater than \(-1.5\)).

3. For \(k = -\frac{3}{2}\):
\(-\frac{3}{2} > -\frac{3}{2}\) is **false** (it's not greater, it's equal).

4. For \(k = -5\):
\(-5 > -\frac{3}{2}\) is **false** (since \(-5\) is much less than \(-1.5\)).

The only value from the given options that satisfies the inequality \(k > -\frac{3}{2}\) is:

\[
\boxed{-1}
\]