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We are tasked with finding the length of segment \( \overline{ST} \) using the Segment Addition Postulate. The Segment Addition Postulate states that if point \( S \) is between \( R \) and \( T \), then:

\[
\overline{RT} = \overline{RS} + \overline{ST}
\]

From the given problem:

- \( \overline{SR} = 2x + 7 \)
- \( \overline{ST} = x - 6 \)
- \( \overline{RT} = 100 \)

Using the Segment Addition Postulate, we can set up the equation:

\[
\overline{RT} = \overline{SR} + \overline{ST}
\]

Substituting the values:

\[
100 = (2x + 7) + (x - 6)
\]

Now, let's solve for \( x \):

\[
100 = 2x + 7 + x - 6
\]
\[
100 = 3x + 1
\]
\[
100 - 1 = 3x
\]
\[
99 = 3x
\]
\[
x = \frac{99}{3} = 33
\]

Now that we have \( x = 33 \), we can find \( \overline{ST} \):

\[
\overline{ST} = x - 6 = 33 - 6 = 27
\]

Thus, the length of \( \overline{ST} \) is **27 units**.

Do you want any further clarification or details?

Here are 5 related questions to consider:
1. How would the equation change if \( \overline{SR} \) was a constant value instead of a function of \( x \)?
2. How does the Segment Addition Postulate apply to non-collinear points?
3. What would happen if the total length \( \overline{RT} \) was unknown?
4. How would you solve this problem graphically by plotting the points on a coordinate plane?
5. How does the concept of midpoint relate to segment addition?

**Tip:** Always recheck each step in algebraic manipulation, as small errors in sign can lead to incorrect results.

Use the Segment Addition Postulate to find the length of ST if SR = 2x + 7, ST = x - 6, and RT = 100.

Learn how to find the length of ST using the Segment Addition Postulate with an algebraic approach. The problem involves solving for x given SR = 2x + 7, ST = x - 6, and RT = 100. Suitable for students in Grades 8-10.

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