Let's solve the equation \(-4(v + 3) - 3v = 2(v + 3)\).

1. **Distribute** the constants through the parentheses:
   \[
   -4 \cdot (v + 3) - 3v = 2 \cdot (v + 3)
   \]
   This simplifies to:
   \[
   -4v - 12 - 3v = 2v + 6
   \]

2. **Combine like terms** on the left side:
   \[
   -4v - 3v - 12 = 2v + 6
   \]
   Which simplifies to:
   \[
   -7v - 12 = 2v + 6
   \]

3. **Move all terms involving** \(v\) to one side and constants to the other:
   \[
   -7v - 2v = 6 + 12
   \]
   Simplifying this gives:
   \[
   -9v = 18
   \]

4. **Solve for** \(v\) by dividing both sides by \(-9\):
   \[
   v = \frac{18}{-9} = -2
   \]

So, the solution is \(v = -2\).

Would you like more details, or do you have any questions?

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Here are some related questions you might find useful:

1. How do you check if the solution \(v = -2\) satisfies the original equation?
2. What happens if you transpose terms in different steps?
3. How do you solve equations with fractions?
4. Can this method be used for equations with higher powers of \(v\)?
5. How does the solution change if the equation has no constant term?
6. What if the equation were quadratic instead of linear?
7. How do you solve equations with absolute values?
8. How do you interpret the solution of a system of equations graphically?

**Tip:** Always double-check your solution by substituting it back into the original equation.

Learn how to solve the linear equation -4(v + 3) - 3v = 2(v + 3) step-by-step. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 7-9.

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