Question

if pq = 4x, qr = x + 3, and pr = 6x − 5, what is pr?
diagram: p---q---r with pq labeled 4x, qr labeled x + 3, pr labeled 6x − 5
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( PQ + QR = PR \). Substitute the given expressions: \( 4x + (x + 3) = 6x - 5 \).

Step2: Simplify left side

Combine like terms: \( 5x + 3 = 6x - 5 \).

Step3: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 3 = x - 5 \). Then add 5 to both sides: \( x = 8 \).

Step4: Find \( PR \)

Substitute \( x = 8 \) into \( PR = 6x - 5 \): \( PR = 6(8) - 5 = 48 - 5 = 43 \).

Answer:

43