https://file.aiquickdraw.com/mathbot/file/172611105778167kg82oq.jpg

The problem provided in the image asks you to find \( PR \) given the following two segments:

- \( PQ = 6x + 25 \)
- \( QR = 16 - 3x \)

Since \( P \), \( Q \), and \( R \) are collinear points, we can express \( PR \) as:

\[
PR = PQ + QR
\]

Let's substitute the values for \( PQ \) and \( QR \):

\[
PR = (6x + 25) + (16 - 3x)
\]

Now, we can simplify the expression:

\[
PR = 6x + 25 + 16 - 3x
\]
\[
PR = 3x + 41
\]

Thus, \( PR = 3x + 41 \).

Would you like me to explain any part of this further, or go into details about solving for \( x \) if more information is provided?

Here are 5 questions related to the topic:
1. How would you solve for \( x \) if \( PR \) were given a specific value?
2. How can you use the concept of collinearity to solve problems involving line segments?
3. What are the implications if \( PR \) is negative?
4. How would you approach finding \( x \) in a system where \( PQ = QR \)?
5. What are some real-world applications of this type of algebraic reasoning?

**Tip**: Always check the relationships between given segments (like addition of collinear segments) to ensure the equations are set up correctly.

Learn how to find PR by using collinear points and algebraic expressions for PQ and QR. The problem involves adding linear equations and simplifying the result. Suitable for students in Grades 6-8.

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