Point Q is on line segment PR. Given PR = 2x, PQ = 5x - 4, and QR = x, determine the numerical length of PR

We are given that:

- \( PR = 2x \)
- \( PQ = 5x - 4 \)
- \( QR = x \)

Since \( PQ + QR = PR \) (because \( Q \) is on line segment \( PR \)), we can write the equation:

\[
PQ + QR = PR
\]

Substituting the given values:

\[
(5x - 4) + x = 2x
\]

Now, simplify the equation:

\[
6x - 4 = 2x
\]

Subtract \( 2x \) from both sides:

\[
4x - 4 = 0
\]

Add 4 to both sides:

\[
4x = 4
\]

Divide by 4:

\[
x = 1
\]

Now, substitute \( x = 1 \) into the expression for \( PR \):

\[
PR = 2x = 2(1) = 2
\]

Thus, the numerical length of \( PR \) is \( 2 \).

Would you like more details on any step or have any further questions? Here are some related questions to explore:

1. What would change if \( QR \) were given as \( 2x \) instead of \( x \)?
2. How would the solution differ if \( PQ \) were negative?
3. What happens if point \( Q \) divides \( PR \) in a 3:2 ratio?
4. Can you find the lengths of \( PQ \) and \( QR \) after solving for \( x \)?
5. How would this process change if \( PR \) was an unknown constant instead of \( 2x \)?

**Tip:** When solving problems involving segments, always use the sum of smaller segments to express the full segment length as an equation.

Point Q is on line segment PR. Given PR = 2x, PQ = 5x - 4, and QR = x, determine the numerical length of PR.

Learn how to solve a geometry problem involving algebraic expressions to determine the length of a line segment. Given PR = 2x, PQ = 5x - 4, and QR = x, this step-by-step solution guides you through using the Segment Addition Postulate. Suitable for Grades 6-8.

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