Question

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

Explanation:

Step1: Divide both sides by -3 (reverse inequality)

Divide each side of \(-3(4k + 1) < 15\) by \(-3\). Remember, when dividing an inequality by a negative number, the inequality sign flips. So we get \(4k + 1 > \frac{15}{-3}\), which simplifies to \(4k + 1 > -5\).

Step2: Subtract 1 from both sides

Subtract 1 from each side of \(4k + 1 > -5\): \(4k + 1 - 1 > -5 - 1\), which simplifies to \(4k > -6\).

Step3: Divide both sides by 4

Divide each side of \(4k > -6\) by 4: \(k > \frac{-6}{4}\), which simplifies to \(k > -\frac{3}{2}\) (or \(k > -1.5\)).

Now we check each option:

• For \(\frac{-3}{2} = -1.5\): \(k > -1.5\), so \(-1.5\) is not in the solution set (since it's equal, not greater).
• For \(-5\): \(-5 < -1.5\), so not in the solution set.
• For \(-1\): \(-1 > -1.5\), so \(-1\) is in the solution set.
• For \(-4\): \(-4 < -1.5\), so not in the solution set.

Answer:

\(\boldsymbol{-1}\) (the option corresponding to -1)