https://file.aiquickdraw.com/mathbot/file/1726188396814iplqahwd.jpg

The problem shows a segment \( HE \), with points \( G \) and \( F \) between \( H \) and \( E \). The lengths of different segments along this line are represented by the following algebraic expressions:

- \( HG = 13x - 993 \)
- \( GF = 3x - 129 \)
- \( FE = 3x - 185 \)
- \( EF = 4 \)

To find \( GE \), we can express \( GE \) as the sum of the segments \( GF \) and \( FE \). 

So, we have:
\[
GE = GF + FE
\]
Substitute the expressions for \( GF \) and \( FE \):
\[
GE = (3x - 129) + (3x - 185)
\]
Simplifying:
\[
GE = 3x - 129 + 3x - 185 = 6x - 314
\]

Thus, the length of \( GE \) is \( 6x - 314 \).

Would you like to proceed by solving for \( x \), or do you want further details on the steps? Here are some follow-up questions:

1. How do we solve for \( x \) if we know the total length of \( HE \)?
2. How can we express the length of \( HE \) in terms of \( x \)?
3. What additional steps are needed to solve for \( GE \) once \( x \) is found?
4. How does knowing the value of \( FE \) help solve the problem?
5. How do you verify the accuracy of the solution?

**Tip:** When solving problems with segments, always add smaller segments to express the larger segment.

Find GE, where the segment HE is divided into segments: HG = 13x - 993, GF = 3x - 129, FE = 3x - 185, and EF = 4.

Solve a geometry problem to find the length of GE by using algebraic expressions for GF and FE. Learn how to combine segments with expressions like GF = 3x - 129 and FE = 3x - 185 to determine GE in terms of x.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation