We are given the compound inequality:

\[
-16 < 6k + 2 < 0
\]

### Step 1: Isolate the \( k \)-term in the inequality.

To do this, we will first subtract 2 from all parts of the inequality.

\[
-16 - 2 < 6k + 2 - 2 < 0 - 2
\]

Simplifying this gives:

\[
-18 < 6k < -2
\]

### Step 2: Solve for \( k \).

Next, divide the entire inequality by 6 to isolate \( k \).

\[
\frac{-18}{6} < \frac{6k}{6} < \frac{-2}{6}
\]

Simplifying:

\[
-3 < k < -\frac{1}{3}
\]

### Final Answer:

The solution to the inequality is:

\[
-3 < k < -\frac{1}{3}
\]

This means that \( k \) must be greater than \(-3\) but less than \(-\frac{1}{3}\).

Do you have any questions or would you like further details on this solution?

Here are some related questions for practice:

1. Solve: \( -10 < 4k + 1 < 5 \).
2. Solve: \( -20 < 3k + 4 < 1 \).
3. Solve: \( -12 < 5k - 2 < 3 \).
4. Solve: \( -8 < 2k - 6 < 4 \).
5. Solve: \( -15 < 7k + 5 < 10 \).

**Tip:** When solving compound inequalities, remember to perform the same operations on all three parts of the inequality to maintain balance.

Learn how to solve the compound inequality -16 < 6k + 2 < 0 with a clear, step-by-step breakdown. This problem involves key algebraic concepts, including isolating variables and solving inequalities. Suitable for students in Grades 7-9.

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