If RS = 2x, ST = x + 5, and RT = 8, what is RS?

We are given:

- \( RS = 2x \)
- \( ST = x + 5 \)
- \( RT = 8 \)

Since points \( R, S, T \) are on the same line, the total length \( RT \) is the sum of \( RS \) and \( ST \):

\[
RS + ST = RT
\]

Substitute the given values:

\[
2x + (x + 5) = 8
\]

Now, solve for \( x \):

\[
2x + x + 5 = 8
\]
\[
3x + 5 = 8
\]
\[
3x = 8 - 5
\]
\[
3x = 3
\]
\[
x = 1
\]

Now substitute \( x = 1 \) back into \( RS = 2x \):

\[
RS = 2(1) = 2
\]

So, the value of \( RS \) is 2.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is the length of \( ST \) when \( x = 1 \)?
2. What would \( RS \) be if \( RT = 10 \)?
3. If \( ST = 2x + 4 \), how would you solve for \( RS \)?
4. Can you apply this method to solve for distances between non-collinear points?
5. How would you graph these points on a number line?

**Tip**: Always combine like terms early in equations to simplify the solving process.

Discover how to solve for RS when given RS = 2x, ST = x + 5, and RT = 8. This algebra problem uses the Segment Addition Postulate and solving linear equations, ideal for students in Grades 6-8.

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