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!