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To solve the problem where \( M \) is the midpoint of \( \overline{FG} \), we know the following:

- \( FM = 3x - 4 \)
- \( MG = 5x - 26 \)

Since \( M \) is the midpoint, we have \( FM = MG \). We can set up the equation:

\[
3x - 4 = 5x - 26
\]

Now, let's solve for \( x \):

\[
3x - 5x = -26 + 4
\]

\[
-2x = -22
\]

\[
x = 11
\]

Now that we have \( x = 11 \), we can find the length of \( \overline{FG} \) by adding \( FM \) and \( MG \):

\[
FM = 3x - 4 = 3(11) - 4 = 33 - 4 = 29
\]
\[
MG = 5x - 26 = 5(11) - 26 = 55 - 26 = 29
\]

Since \( FM = 29 \) and \( MG = 29 \), the total length of \( \overline{FG} \) is:

\[
FG = FM + MG = 29 + 29 = 58
\]

So, the length of \( \overline{FG} \) is **58**.

Would you like further details on this solution, or do you have any other questions?

Here are 5 related questions:
1. How would the solution change if \( FM \) and \( MG \) were not equal?
2. Can you apply the midpoint formula in coordinate geometry to find the midpoint \( M \)?
3. What if \( M \) were not the midpoint but a different point on \( \overline{FG} \)?
4. How does this problem relate to the segment addition postulate?
5. How would you find \( FG \) if the expressions for \( FM \) and \( MG \) were quadratic?

**Tip:** When dealing with midpoint problems, always remember that the lengths of the two segments are equal if one point is indeed the midpoint.

Suppose M is the midpoint of FG. Find the missing measure. FM = 3x - 4, MG = 5x - 26. What is FG?

Learn how to find the length of FG given that M is the midpoint, with expressions for FM and MG. This problem covers algebraic concepts like solving linear equations and applying the Midpoint Theorem, suitable for students in Grades 7-9.

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