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The problem asks us to use the Segment Addition Postulate to find the length of \( ST \).

Given:
- \( RS = 2x + 14 \)
- \( ST = 3x - 6 \)
- \( RT = 53 \)

Using the **Segment Addition Postulate**, we know:
\[
RS + ST = RT
\]
Substitute the given expressions:
\[
(2x + 14) + (3x - 6) = 53
\]
Now solve for \( x \):

1. Combine like terms:
\[
2x + 3x + 14 - 6 = 53
\]
\[
5x + 8 = 53
\]

2. Subtract 8 from both sides:
\[
5x = 45
\]

3. Divide by 5:
\[
x = 9
\]

Now that we know \( x = 9 \), we can substitute it back into the expression for \( ST \) to find its length:
\[
ST = 3x - 6 = 3(9) - 6 = 27 - 6 = 21
\]

Thus, the length of \( ST \) is **21 units**.

Let me know if you want any details or explanations on any step!

Here are 5 related questions for further practice:
1. If \( RS = 3x + 5 \) and \( ST = 2x + 7 \), and \( RT = 50 \), what is the value of \( x \)?
2. Can you derive the equation for \( RS + ST = RT \) from the diagram alone?
3. How would the solution change if \( RT = 45 \) instead of \( 53 \)?
4. What does the Segment Addition Postulate imply about points on a straight line?
5. Can you verify the result by checking all segment lengths?

**Tip:** Always substitute the found values back into the original expressions to ensure the calculations are consistent!

Use the Segment Addition Postulate to find the length of ST. Given RS = 2x + 14, ST = 3x - 6, and RT = 53.

Solve for the length of ST using the Segment Addition Postulate. Given RS = 2x + 14, ST = 3x - 6, and RT = 53. Step-by-step solution provided with key algebraic concepts for students in Grades 8-10.

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