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The image shows a geometric line segment with points labeled \( F \), \( G \), and \( H \). The distances are given as algebraic expressions:

- The distance between \( F \) and \( G \) is represented as \( 11x - 7 \).
- The distance between \( G \) and \( H \) is represented as \( 3x + 9 \).

It appears that the total distance from \( F \) to \( H \) might be implied to form an equation, but the total length is not explicitly given in the image.

To solve this, we would likely need to combine the expressions \( FG \) and \( GH \) and set them equal to the total length of \( FH \) (if it's provided or can be inferred).

Do you have any additional information or a specific total length for the segment \( FH \)? Would you like me to proceed with an assumption or provide a detailed solution for any part of this? Let me know!

Here are some questions that could further explore the concept:
1. How would you solve for \( x \) if the total length of segment \( FH \) was given?
2. What happens if \( FG + GH \) equals zero? Can \( x \) be determined?
3. How do you combine algebraic expressions to form an equation for a line segment?
4. What real-life situations might require combining distances expressed as algebraic terms?
5. Can you create a scenario where algebraic distances are combined for multiple segments in a geometry problem?

**Tip:** When combining distances expressed algebraically, make sure to simplify terms carefully before solving for unknowns like \( x \).

The distance between F and G is given as 11x - 7 and the distance between G and H is given as 3x + 9. Solve for x or provide the total length of FH if available.

Learn how to solve for x when combining algebraic expressions for distances between points F, G, and H on a line segment. This problem explores key algebraic concepts in geometry, using the segment addition postulate.

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