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The problem gives us three conditions:

1. \( EF = 8x - 17 \)
2. \( FG = 9x - 6 \)
3. \( EG = 62 \)

Since \( E, F, G \) are points on a line, we know that the total distance \( EG \) is the sum of \( EF \) and \( FG \). Thus:

\[
EG = EF + FG
\]

Substituting the given expressions for \( EF \) and \( FG \):

\[
62 = (8x - 17) + (9x - 6)
\]

Let's solve this step by step.

\[
62 = 8x - 17 + 9x - 6
\]
\[
62 = 17x - 23
\]
\[
62 + 23 = 17x
\]
\[
85 = 17x
\]
\[
x = \frac{85}{17} = 5
\]

Now that we have \( x = 5 \), we can find \( EF \) and \( FG \).

1. \( EF = 8x - 17 = 8(5) - 17 = 40 - 17 = 23 \)
2. \( FG = 9x - 6 = 9(5) - 6 = 45 - 6 = 39 \)

So, the values are:
- \( x = 5 \)
- \( EF = 23 \)
- \( FG = 39 \)

Thus, the answer to input would be **5,23,39**.

Would you like a more detailed explanation on any part of the solution?

Here are 5 related questions to expand your understanding:
1. What happens if the total length \( EG \) changes?
2. How would you solve the problem if \( EF \) and \( FG \) were not given as linear expressions?
3. What role does algebra play in geometry problems like this one?
4. How could you solve this geometrically without algebra?
5. How does solving for \( x \) help in determining the lengths of line segments?

**Tip:** When solving for unknowns in geometry problems, always check if the total distance is the sum of its parts—this simplifies the algebra.

If EF = 8x - 17, FG = 9x - 6, and EG = 62, find the values of x, EF, and FG.

Learn how to solve for x, EF, and FG using algebraic expressions. This geometry problem involves linear equations and the Segment Addition Postulate, ideal for students in Grades 8-10.

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