https://file.aiquickdraw.com/mathbot/file/1727101810292s9wrnq1u.jpg

Let's solve the problem in the image.

We are given:

- \( DF = 9x - 39 \)
- \( DE = 47 \)
- \( EF = 3x + 10 \)

The relationship is:

\[
DF = DE + EF
\]

Substituting the given values:

\[
9x - 39 = 47 + (3x + 10)
\]

Now, let's solve this equation:

\[
9x - 39 = 47 + 3x + 10
\]

Simplifying the right side:

\[
9x - 39 = 57 + 3x
\]

Subtract \( 3x \) from both sides:

\[
6x - 39 = 57
\]

Add 39 to both sides:

\[
6x = 96
\]

Divide by 6:

\[
x = 16
\]

Now that we know \( x = 16 \), let's find \( EF \).

Substitute \( x = 16 \) into \( EF = 3x + 10 \):

\[
EF = 3(16) + 10 = 48 + 10 = 58
\]

So, \( EF = 58 \).

Would you like any more details or have any questions?

Here are five related questions to expand on this problem:

1. How would the result change if \( EF \) was expressed as \( 2x + 20 \) instead of \( 3x + 10 \)?
2. What would happen if \( DF \) was expressed in a quadratic form?
3. Can you solve for \( EF \) if \( DF \) were given as a constant number, say 150?
4. What if the equation included more segments on the line, such as an additional point between \( D \) and \( E \)?
5. How do equations change if distances between points are defined in terms of different variables?

**Tip**: Always combine like terms and simplify the equation step by step to avoid mistakes.

If DF = 9x - 39, find EF. DF = DE + EF, where DE = 47 and EF = 3x + 10.

Learn how to solve for EF in the equation DF = 9x - 39, where DF = DE + EF, DE = 47, and EF = 3x + 10. This algebra problem covers key concepts in solving linear equations. Suitable for students in Grades 8-10.

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