point q is on line segment PR. given PQ = x, QR =6, and PR = 2x-10, determine the numerical length of PQ

We are given that point \( Q \) is on line segment \( PR \), and the following distances:

- \( PQ = x \)
- \( QR = 6 \)
- \( PR = 2x - 10 \)

Since \( Q \) is a point on the segment \( PR \), the total length of \( PR \) should be equal to the sum of \( PQ \) and \( QR \). Therefore, we can write the equation:

\[
PQ + QR = PR
\]

Substitute the given values into this equation:

\[
x + 6 = 2x - 10
\]

Now, solve for \( x \):

\[
6 + 10 = 2x - x
\]
\[
16 = x
\]

So, the length of \( PQ \) is \( \boxed{16} \).

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. If \( QR \) was \( 8 \) instead of \( 6 \), what would the new value of \( PQ \) be?
2. What is the total length of \( PR \) if \( PQ = 16 \) and \( QR = 6 \)?
3. If \( PR = 50 \) and \( QR = 20 \), find \( PQ \) using the same method.
4. How would the problem change if \( PR \) was given as \( 3x - 12 \) instead of \( 2x - 10 \)?
5. What is the relationship between the lengths of segments in any general line segment division?

**Tip:** When solving geometry problems with line segments, always remember that the total length of a segment is the sum of its parts.

Point Q is on line segment PR. Given PQ = x, QR = 6, and PR = 2x - 10, determine the numerical length of PQ.

Learn how to find the length of line segment PQ when given PR = 2x - 10 and QR = 6. This geometry problem involves using algebraic expressions and the Segment Addition Postulate. Suitable for students in Grades 6-8.

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