https://file.aiquickdraw.com/mathbot/file/1726794375369i1px9zpq.jpg

Let's analyze the problem step-by-step:

We are given:

- \( RS = 3x \)
- \( ST = x + 11 \)
- \( RT = 19 \)

From the diagram, it's clear that \( R \), \( S \), and \( T \) are collinear points, meaning:

\[
RS + ST = RT
\]

Substituting the values:

\[
3x + (x + 11) = 19
\]

Now, let's solve this equation:

\[
3x + x + 11 = 19
\]
\[
4x + 11 = 19
\]
\[
4x = 19 - 11
\]
\[
4x = 8
\]
\[
x = 2
\]

Now that we have \( x = 2 \), we can find \( ST \):

\[
ST = x + 11 = 2 + 11 = 13
\]

Thus, the length of \( ST \) is **13** units.

Would you like a deeper explanation, or do you have any questions about this solution?

Here are 5 related questions to extend your understanding:
1. What is the length of \( RS \) with the value of \( x \) found?
2. How would the solution change if \( RT \) were a different value, say 25?
3. What would the equation look like if \( ST \) were expressed as a function of \( RS \)?
4. How can you verify if \( RS + ST = RT \) holds true after solving for \( x \)?
5. If a new point \( U \) is added such that \( ST = 2 \times TU \), how would you find \( TU \)?

**Tip:** When solving linear equations, always check if combining like terms simplifies the problem significantly.

If RS = 3x, ST = x + 11, and RT = 19, what is ST?

Learn how to solve a linear equation involving line segments. In this example, you will find the length of ST, given RS = 3x, ST = x + 11, and RT = 19. Suitable for students in Grades 7-8.

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