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In the given diagram, you are asked to find the length of segment \( GE \). The segment \( GE \) is divided into two parts: \( GF \) and \( FE \). 

- \( GF = 2x + 23 \)
- \( FE = x + 21 \)
- The entire length of \( GE = GF + FE \)

We can set up the following equation to find the total length of \( GE \):

\[
GE = GF + FE = (2x + 23) + (x + 21)
\]

Simplifying the equation:

\[
GE = 2x + 23 + x + 21 = 3x + 44
\]

Thus, the length of segment \( GE \) is \( 3x + 44 \). If \( x \) is known, you can substitute its value to get the exact length.

Would you like further assistance on how to solve for \( x \) or any other part of the problem? 

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Here are 5 related questions to expand your understanding:

1. How would the length of \( GE \) change if the values of \( GF \) and \( FE \) were different?
2. What happens to the equation if \( GF \) is greater than \( FE \)?
3. How can you find \( x \) if you are given the total length of segment \( GE \)?
4. How do you solve equations with variables on both sides, like in this case?
5. What are the steps to verify the correctness of the solution?

**Tip:** When dealing with segment addition, remember that the total length of the larger segment equals the sum of its smaller parts!

Learn how to find the length of segment GE, where GF = 2x + 23 and FE = x + 21. The problem involves applying the segment addition postulate and solving algebraic expressions. Suitable for students in Grades 8-10.

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