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Let's go through each equation to determine whether it has no solution, one solution, or infinitely many solutions.

1. **\( 8v + 3 - 4v = 4v + 5 - 2 \)**  
   Simplify both sides:
   \[
   8v - 4v + 3 = 4v + 3
   \]
   \[
   4v + 3 = 4v + 3
   \]
   Subtract \( 4v \) from both sides:
   \[
   3 = 3
   \]
   Since this is a true statement, the equation has **infinitely many solutions**.

2. **\( 7v - 11 = 7v + 11 \)**  
   Subtract \( 7v \) from both sides:
   \[
   -11 = 11
   \]
   This is a contradiction, so the equation has **no solution**.

3. **\( 3(v - 4) = 2(v - 6) \)**  
   Expand both sides:
   \[
   3v - 12 = 2v - 12
   \]
   Subtract \( 2v \) from both sides:
   \[
   v - 12 = -12
   \]
   Add 12 to both sides:
   \[
   v = 0
   \]
   This equation has **one solution**.

4. **\( 5(2v + 3) - 2 = 12v + 12 - 2v \)**  
   Expand both sides:
   \[
   10v + 15 - 2 = 12v + 12 - 2v
   \]
   Simplify:
   \[
   10v + 13 = 10v + 12
   \]
   Subtract \( 10v \) from both sides:
   \[
   13 = 12
   \]
   This is a contradiction, so the equation has **no solution**.

### Summary of the solutions:
1. Infinitely Many Solutions
2. No Solution
3. One Solution
4. No Solution

Would you like a more detailed explanation on any of these steps?

Here are 5 related questions you could explore:
1. How do you determine when an equation has no solution?
2. What does it mean for an equation to have infinitely many solutions?
3. How can systems of equations be used to solve real-world problems?
4. What are the differences between dependent and independent systems in algebra?
5. How do you solve systems of linear equations graphically?

**Tip:** Always simplify both sides of the equation before deciding on the number of solutions, and check for contradictions or true statements.

Select No Solution, One Solution, or Infinitely Many Solutions for each equation: 8v + 3 - 4v = 4v + 5 - 2, 7v - 11 = 7v + 11, 3(v - 4) = 2(v - 6), and 5(2v + 3) - 2 = 12v + 12 - 2v.

Learn how to determine whether linear equations with variables on both sides have no solution, one solution, or infinitely many solutions. This problem covers key algebraic concepts, such as simplifying equations and solving linear equations by combining like terms and using the distributive property.

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