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?

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!