Let's solve the equation:

\[
-6v - 27 = 9(v + 7)
\]

### Step 1: Distribute the \(9\) on the right-hand side:
\[
-6v - 27 = 9v + 63
\]

### Step 2: Move all terms involving \(v\) to one side. Subtract \(9v\) from both sides:
\[
-6v - 9v - 27 = 63
\]
\[
-15v - 27 = 63
\]

### Step 3: Move the constant term \(-27\) to the right-hand side. Add \(27\) to both sides:
\[
-15v = 63 + 27
\]
\[
-15v = 90
\]

### Step 4: Solve for \(v\) by dividing both sides by \(-15\):
\[
v = \frac{90}{-15}
\]
\[
v = -6
\]

### Final Solution:
\[
v = -6
\]

Would you like more details or have any questions?

Here are five related questions:
1. What happens if you substitute \(v = -6\) back into the original equation?
2. How would the solution change if the equation were \( -6v - 27 = 9(v + 8) \)?
3. Can you graph both sides of the equation and interpret where they intersect?
4. What is the importance of distributing before combining like terms?
5. How would the solution change if the equation included a squared term for \(v\)?

**Tip:** Always simplify both sides of an equation as much as possible before solving for the variable.

Learn how to solve the linear equation -6v - 27 = 9(v + 7) step by step. This problem involves applying the distributive property and combining like terms to find the solution v = -6. Suitable for students in Grades 6-8.

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