3

(

3

+

3

v

)

=

–

2

(

9

–

3

v

)

Let's solve the equation step by step.

### Given equation:
\[
3(3 + 3v) = -2(9 - 3v)
\]

### Step 1: Distribute the constants to the terms inside the parentheses on both sides of the equation.
- On the left side, distribute \(3\):
\[
9 + 9v
\]
- On the right side, distribute \(-2\):
\[
-18 + 6v
\]

So the equation becomes:
\[
9 + 9v = -18 + 6v
\]

### Step 2: Get all the \(v\) terms on one side and constant terms on the other side.
- Subtract \(6v\) from both sides:
\[
9 + 3v = -18
\]

### Step 3: Isolate the variable \(v\).
- Subtract 9 from both sides:
\[
3v = -27
\]

- Divide both sides by 3:
\[
v = -9
\]

### Final Answer:
\[ v = -9 \]

Would you like more details on any of these steps or have any questions?

Here are some related questions you might find interesting:
1. How do you solve equations involving distribution?
2. What are the steps to isolate a variable in an equation?
3. How do you handle negative coefficients in equations?
4. What happens when you combine like terms with variables on both sides?
5. How can you check if your solution to an equation is correct?

**Tip:** When dealing with negative signs during distribution, be extra careful to apply the negative sign correctly to each term inside the parentheses.

Learn how to solve the equation 3(3 + 3v) = -2(9 - 3v) step-by-step. Understand the process of distributing constants, isolating variables, and solving for v. Suitable for high school students.

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