We are tasked with solving the equation:

\[
-18 - 6k = 6(1 + 3k)
\]

### Step 1: Expand the right-hand side
Distribute the \(6\) on the right-hand side:

\[
-18 - 6k = 6 \cdot 1 + 6 \cdot 3k
\]

This simplifies to:

\[
-18 - 6k = 6 + 18k
\]

### Step 2: Move all terms involving \(k\) to one side
Add \(6k\) to both sides:

\[
-18 = 6 + 18k + 6k
\]

Simplify the right-hand side:

\[
-18 = 6 + 24k
\]

### Step 3: Move constants to one side
Subtract \(6\) from both sides:

\[
-18 - 6 = 24k
\]

Simplifying the left-hand side:

\[
-24 = 24k
\]

### Step 4: Solve for \(k\)
Now divide both sides by 24:

\[
k = \frac{-24}{24} = -1
\]

### Final Answer:
\[
k = -1
\]

Would you like more details on any step, or have any further questions?

Here are 5 related questions you might find helpful:
1. What if the equation was \( -18 - 6k = 12(1 + 3k) \)?
2. How would you solve \( 5k - 2 = 3(k + 4) \)?
3. What happens if we have \( k^2 \) terms in the equation?
4. How do you solve a system of equations involving \( k \)?
5. How does distributing a negative sign affect equations?

**Tip**: Always simplify equations step-by-step to avoid errors, especially when distributing terms across parentheses.

Explore how to solve the linear equation -18 - 6k = 6(1 + 3k) step-by-step. This problem demonstrates the distributive property and techniques for solving linear equations. Perfect for students in Grades 7-9.

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