Point H is on line segment GI. Given GI = 5x, HI = 3x - 8, and GH = 3x, determine the numerical length of GH

We are given three segments on the line: GI, HI, and GH. Let's express each segment in terms of \( x \) based on the information provided.

- \( GI = 5x \)
- \( HI = 3x - 8 \)
- \( GH = 3x \)

Since point \( H \) lies on line segment \( GI \), we know that:

\[
GH + HI = GI
\]

Substitute the expressions for \( GH \), \( HI \), and \( GI \):

\[
3x + (3x - 8) = 5x
\]

Simplify the left-hand side:

\[
6x - 8 = 5x
\]

Now, solve for \( x \):

\[
6x - 5x = 8
\]
\[
x = 8
\]

Now that we know \( x = 8 \), substitute this value back into the expression for \( GH \):

\[
GH = 3x = 3(8) = 24
\]

Thus, the numerical length of \( GH \) is **24 units**.

Would you like further explanation or details?

Here are 5 related questions for practice:
1. What is the numerical length of \( GI \)?
2. What is the numerical length of \( HI \)?
3. If \( H \) divides \( GI \) in the ratio of \( GH:HI \), what is that ratio?
4. If \( GH = 24 \) and \( HI = 16 \), what is the total length of \( GI \)?
5. Can you find \( x \) if \( GI = 10x \), \( GH = 6x \), and \( HI = 4x - 5 \)?

**Tip:** Always check if a point lies on a line segment by verifying that the sum of the smaller segments equals the total length.

Point H is on line segment GI. Given GI = 5x, HI = 3x - 8, and GH = 3x, determine the numerical length of GH.

Learn how to determine the length of segment GH when given GI = 5x, HI = 3x - 8, and GH = 3x. This problem uses algebraic concepts and the Segment Addition Postulate, suitable for students in Grades 8-10.

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