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

Question

Responses

−5
negative 5

−32
Start Fraction negative 3 over 2 End Fraction

−4
negative 4

−1

Answer 1

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

\[ -12k - 3 < 15 \]

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:

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

So, the solution set is \(k > -\frac{3}{2}\).

Now we will check the response options to see which one satisfies this condition:

1. \(-5\): This is less than \(-\frac{3}{2}\), so it doesn't satisfy the inequality.
2. \(-32\): This is also less than \(-\frac{3}{2}\).
3. \(-4\): This is still less than \(-\frac{3}{2}\).
4. \(-1\): This is greater than \(-\frac{3}{2}\).

Thus, the value that falls in the solution set of the inequality is:

\(-1\).