https://file.aiquickdraw.com/mathbot/file/1725986294868v2vyv8aw.jpg

The equation presented in the image is:

\[
2(v + 1) = 8
\]

### Steps to solve for \( v \):

1. First, divide both sides by 2 to isolate the \( v + 1 \) term:
   \[
   \frac{2(v + 1)}{2} = \frac{8}{2}
   \]
   Simplifying this gives:
   \[
   v + 1 = 4
   \]

2. Subtract 1 from both sides to solve for \( v \):
   \[
   v = 4 - 1
   \]
   \[
   v = 3
   \]

### Solution:
\[
v = 3
\]

Would you like more details on any step? Here are five additional related questions for practice:

1. What would the equation be if \( 2(v + 1) = 10 \)?
2. Solve \( 3(v + 2) = 12 \).
3. How would you handle \( 4(v - 1) = 16 \)?
4. Can you solve \( 5(v + 3) = 25 \)?
5. How do you solve an equation like \( 6(v + 2) = 18 \)?

**Tip:** When solving linear equations, always perform the same operation on both sides of the equation to maintain equality.

This step-by-step solution demonstrates how to solve the linear equation 2(v + 1) = 8. The problem uses basic algebra to isolate the variable and solve for v. Suitable for Grades 6-8, this example highlights essential skills in solving simple linear equations.

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