If PQ = 8, QR = x − 8, and PR = 2x − 14, what is QR?

Given the information:

- \( PQ = 8 \)
- \( QR = x - 8 \)
- \( PR = 2x - 14 \)

Assuming \( P \), \( Q \), and \( R \) are points on a straight line, we can use the property that the sum of the two smaller segments is equal to the entire segment, so:

\[
PQ + QR = PR
\]

Substituting the given values:

\[
8 + (x - 8) = 2x - 14
\]

Simplify and solve for \( x \):

\[
x = 2x - 14
\]

\[
14 = x
\]

Now that we have \( x = 14 \), substitute it back into the expression for \( QR \):

\[
QR = x - 8 = 14 - 8 = 6
\]

So, \( QR = 6 \).

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How do you solve for a variable in an equation?
2. What is the segment addition postulate?
3. How can you verify if points lie on the same line?
4. What are the common properties of linear segments?
5. How does changing the value of \( x \) affect \( QR \) and \( PR \)?

**Tip:** Always double-check your substitutions to ensure accuracy when solving equations!

Learn how to solve a geometry problem involving segments PQ, QR, and PR on a line. This problem applies the Segment Addition Postulate to find the value of segment QR. Suitable for Grades 7-9.

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