https://file.aiquickdraw.com/mathbot/file/17262023070320f361rjz.jpg

We are given the information:

- \( DF = 9x - 39 \)
- The line segment shows that \( DE = 47 \) and \( EF = 3x + 10 \).

To find \( EF \), we'll follow these steps:

1. The total length of \( DF \) can be expressed as:
   \[
   DF = DE + EF
   \]
   Substituting the known values:
   \[
   9x - 39 = 47 + (3x + 10)
   \]

2. Now, solve for \( x \):
   \[
   9x - 39 = 47 + 3x + 10
   \]
   Simplify:
   \[
   9x - 39 = 57 + 3x
   \]
   Subtract \( 3x \) from both sides:
   \[
   6x - 39 = 57
   \]
   Add 39 to both sides:
   \[
   6x = 96
   \]
   Divide by 6:
   \[
   x = 16
   \]

3. Now that we have \( x = 16 \), substitute it into the expression for \( EF \):
   \[
   EF = 3x + 10 = 3(16) + 10 = 48 + 10 = 58
   \]

Thus, the length of \( EF \) is \( 58 \).

Would you like any more details or have further questions?

Here are some related questions:
1. How can you verify the solution by checking \( DF \)?
2. What would happen if \( DE \) were unknown instead of \( EF \)?
3. How does segment addition work geometrically in this problem?
4. Can this method be applied to any type of line segment with different expressions?
5. How does solving for \( x \) affect finding other line segment values?

**Tip**: Always check the total length of the line to confirm your solution.

If DF = 9x - 39, find EF. The line segment shows that DE = 47 and EF = 3x + 10.

Learn how to solve for EF using algebra and segment addition. Given DF = 9x - 39, DE = 47, and EF = 3x + 10, we find the value of x and then calculate EF. Perfect for students in Grades 7-10.

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