Question

if pq = 6, qr = x - 1, and pr = 3x - 17, what is pr? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the number line, \( PQ + QR = PR \). Substitute the given expressions: \( 6 + (x - 1) = 3x - 17 \).

Step2: Simplify and solve for \( x \)

Simplify left side: \( 6 + x - 1 = x + 5 \). So equation is \( x + 5 = 3x - 17 \).
Subtract \( x \) from both sides: \( 5 = 2x - 17 \).
Add 17 to both sides: \( 22 = 2x \).
Divide by 2: \( x = 11 \).

Step3: Find \( PR \)

Substitute \( x = 11 \) into \( PR = 3x - 17 \): \( PR = 3(11) - 17 = 33 - 17 = 16 \).

Answer:

16