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The question asks us to determine the numerical length of \( ST \), given the following information:

- \( ST = 2x + 6 \)
- \( TU = 4 \)
- \( SU = 4x \)

### Step-by-Step Solution:

1. \( S \), \( T \), and \( U \) are points on the same line, and \( T \) is a point between \( S \) and \( U \). Therefore, the length of \( SU \) is the sum of \( ST \) and \( TU \):
   \[
   SU = ST + TU
   \]

2. Substitute the given expressions for \( ST \), \( TU \), and \( SU \):
   \[
   4x = (2x + 6) + 4
   \]

3. Simplify the equation:
   \[
   4x = 2x + 10
   \]

4. Solve for \( x \) by subtracting \( 2x \) from both sides:
   \[
   2x = 10
   \]

5. Divide both sides by 2:
   \[
   x = 5
   \]

6. Now that we know \( x = 5 \), substitute this back into the expression for \( ST \):
   \[
   ST = 2x + 6 = 2(5) + 6 = 10 + 6 = 16
   \]

### Final Answer:
The numerical length of \( ST \) is **16 units**.

Would you like more details or have any questions? Here are some related questions for further practice:

1. If \( ST = 16 \) and \( SU = 4x \), what is the value of \( SU \)?
2. How do you solve for \( TU \) in a similar problem if the relationship changes?
3. What is the sum of the lengths of all line segments if \( T \) is the midpoint of \( SU \)?
4. Can you derive the same result using a different method, such as graphing?
5. How do systems of equations play a role in solving geometric line problems?

**Tip:** Always double-check your equation setup to ensure you're combining segments correctly, especially in problems with multiple variables!

Point T is on line segment SU. Given ST = 2x + 6, TU = 4, and SU = 4x, determine the numerical length of ST.

Learn how to find the numerical length of a line segment ST given the expressions for ST, TU, and SU. This problem uses algebraic methods and the Segment Addition Postulate, suitable for students in Grades 8-10.

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