Question

on a line segment, q is between p and r. if pq = 13, qr = x + 5, and pr = 3x − 12, what is qr? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

Since Q is between P and R, we have \( PQ + QR = PR \). Substituting the given values, we get \( 13 + (x + 5) = 3x - 12 \).

Step2: Simplify and solve for x

Simplify the left side: \( 13 + x + 5 = x + 18 \). So the equation is \( x + 18 = 3x - 12 \). Subtract x from both sides: \( 18 = 2x - 12 \). Add 12 to both sides: \( 30 = 2x \). Divide both sides by 2: \( x = 15 \).

Step3: Find QR

Substitute \( x = 15 \) into \( QR = x + 5 \). So \( QR = 15 + 5 = 20 \).

Answer:

20