https://file.aiquickdraw.com/mathbot/file/1730134551374poguesc6.jpg

Let's solve each equation to determine the correct statement.

### 1. Solving \(-3(x + 4) - 2x = 2(x + 1)\)

1. Distribute \(-3\) and \(2\):
   \[
   -3x - 12 - 2x = 2x + 2
   \]

2. Combine like terms on each side:
   \[
   -5x - 12 = 2x + 2
   \]

3. Move \(2x\) to the left side:
   \[
   -7x - 12 = 2
   \]

4. Add \(12\) to both sides:
   \[
   -7x = 14
   \]

5. Divide by \(-7\):
   \[
   x = -2
   \]

So, the solution is:
   - \(x = -2\)

### 2. Solving \(3(v + 2) + v = 4(v - 1) + 10\)

1. Distribute \(3\) and \(4\):
   \[
   3v + 6 + v = 4v - 4 + 10
   \]

2. Combine like terms on each side:
   \[
   4v + 6 = 4v + 6
   \]

3. Since both sides are identical, this equation is true for all values of \(v\).

So, the solution is:
   - All real numbers are solutions.

### Final Answers:

1. For the first equation, select \(x = -2\).
2. For the second equation, select "All real numbers are solutions."

Would you like a more detailed breakdown or have any questions?

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Here are 5 related questions:

1. How would the solution change if one side had different terms in these equations?
2. What are other types of equations that have "all real numbers" as solutions?
3. How would you solve these equations if they included fractions?
4. What are some examples of equations that have no solution?
5. How can you check if an equation is an identity (true for all values)?

**Tip:** When solving equations, always simplify and combine like terms to make the process easier.

For each equation, choose the statement that describes its solution. If applicable, give the solution.

Learn how to solve linear equations with variables on both sides. This problem demonstrates key algebraic techniques, including distributing, combining like terms, and understanding identities. Suitable for students in Grades 8-10.

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