If 

*RS* = *x* − 4

, 

*ST* = 8

, and 

*RT* = 2*x* − 11

, what is *RT*?

To solve for \( RT \), we can use the relationship between the segments \( RS \), \( ST \), and \( RT \), where:

\[
RS + ST = RT
\]

Substituting the given expressions:

\[
(x - 4) + 8 = 2x - 11
\]

Simplify the left side:

\[
x + 4 = 2x - 11
\]

Next, we'll move all terms involving \( x \) to one side and constant terms to the other side:

\[
4 + 11 = 2x - x
\]

\[
15 = x
\]

Now that we have \( x = 15 \), we can substitute it back into the expression for \( RT \):

\[
RT = 2x - 11 = 2(15) - 11 = 30 - 11 = 19
\]

So, \( RT = 19 \).

Would you like any further details or have any questions?

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Here are 5 related questions to expand your understanding:

1. What would happen if \( ST \) were a variable instead of a constant?
2. How can you verify that your solution is correct?
3. What is the importance of checking the segment relationships in geometry?
4. How would the result change if the equation for \( RT \) were different?
5. Can the same approach be used for non-linear segment equations?

**Tip:** When working with segment equations, clearly identify and write out all relationships between the segments to avoid mistakes during substitution and solving.

Explore how to calculate the segment RT in geometry using given segment relationships RS = x - 4, ST = 8, and RT = 2x - 11. Follow a step-by-step solution method, understanding segment relationships and equation solving. Suitable for Grades 9-12.

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