Question

What value falls in the solution set of the inequality - 3(4k + 1) < 15? (1 point)
3
2
0 -4
0 -5
0 -1

Answer 1

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

\[
-12k - 3 < 15
\]

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 need to reverse the inequality sign:

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

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

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

Now, we can write this as:

\[
k > -1.5
\]

From the options provided, we need to find which values are greater than \(-1.5\):

- **3**: greater than \(-1.5\)
- **2**: greater than \(-1.5\)
- **0**: greater than \(-1.5\)
- **-4**: not greater than \(-1.5\)
- **-5**: not greater than \(-1.5\)
- **-1**: greater than \(-1.5\)

The values that fall in the solution set of the inequality \(-3(4k + 1) < 15\) are:

- 3
- 2
- 0
- -1

Any of these values (3, 2, 0, -1) can be considered a valid answer.