https://file.aiquickdraw.com/mathbot/file/1726274019843mqyck2ne.jpg

The problem in the image states that point \( M \) is the midpoint of line \( VM \) and gives expressions for the lengths \( VM \) and \( MW \) as:

- \( VM = 4x - 1 \)
- \( MW = 3x + 3 \)

Since \( M \) is the midpoint, the lengths \( VM \) and \( MW \) must be equal. Therefore, we can set up the equation:

\[
4x - 1 = 3x + 3
\]

### Solving for \( x \):

1. Subtract \( 3x \) from both sides:
   \[
   4x - 3x - 1 = 3
   \]
   \[
   x - 1 = 3
   \]

2. Add 1 to both sides:
   \[
   x = 4
   \]

### Finding the length of \( VM \):

Substitute \( x = 4 \) back into the expression for \( VM \):

\[
VM = 4x - 1 = 4(4) - 1 = 16 - 1 = 15
\]

Therefore, the length of \( VM \) is **15**.

Would you like further details or have any questions about this? 

Here are 5 related questions you can explore:
1. How do you verify if point \( M \) is truly the midpoint?
2. What is the total length of line \( VW \)?
3. Can you solve similar problems where the midpoint's coordinates are given?
4. How can we determine if two line segments are congruent geometrically?
5. What if \( VM \) and \( MW \) had been different lengths?

**Tip:** Always remember that for midpoint problems, the two segments on either side of the midpoint are equal in length.

Point M is the midpoint of line VM. Find the length of line VM. The expressions for VM and MW are given as VM = 4x - 1 and MW = 3x + 3.

Learn how to solve the algebra problem where point M is the midpoint of line VM. Given the expressions VM = 4x - 1 and MW = 3x + 3, solve for the length of VM. This solution covers key concepts in algebra and the midpoint theorem. Suitable for students in Grades 6-8.

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