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

Answer 1

To solve the inequality \(-3(4k + 1) < 15\), we can follow these steps:

1. Distribute \(-3\) on the left side: \[ -12k - 3 < 15 \]

2. Add \(3\) to both sides to isolate the term involving \(k\): \[ -12k < 15 + 3 \] \[ -12k < 18 \]

3. Divide both sides by \(-12\). Remember that dividing by a negative number reverses the inequality: \[ k > \frac{18}{-12} \] \[ k > -\frac{3}{2} \]

The solution set of the inequality is all values of \(k\) that are greater than \(-\frac{3}{2}\).

Any value greater than \(-1.5\) falls in this solution set. Some examples include \(0\), \(1\), \(2\), or specifically any number like \(-1\).

To summarize, any \(k\) value greater than \(-\frac{3}{2}\) satisfies the original inequality.