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

Question

-5
-3/2
-1
-4

Answer 1

To solve the inequality \(-3(4k + 1) < 15\), we will start by simplifying it step by step.

1. Distribute \(-3\): \[ -12k - 3 < 15 \]

2. Add 3 to both sides: \[ -12k < 15 + 3 \] \[ -12k < 18 \]

3. Divide by \(-12\) and remember to flip the inequality sign: \[ k > \frac{18}{-12} \] \[ k > -\frac{3}{2} \]

From this, we see that the solution set is: \[ k > -\frac{3}{2} \]

Now let's see which of the given values falls within this range:

• -5: This is not greater than \(-\frac{3}{2}\).
• -\frac{3}{2}: This is not greater than \(-\frac{3}{2}\) (it is equal).
• -1: This is greater than \(-\frac{3}{2}\).
• -4: This is not greater than \(-\frac{3}{2}\).

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

\[ \boxed{-1} \]