Question

if pq = 7x, qr = 13x − 4, and pr = 19x + 15, what is pr? diagram of line segment p---q---r with pq labeled 7x, qr labeled 13x - 4, pr labeled 19x + 15 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: \( 7x + (13x - 4) = 19x + 15 \).

Step2: Simplify left side

Combine like terms: \( 7x + 13x - 4 = 20x - 4 \). So the equation is \( 20x - 4 = 19x + 15 \).

Step3: Solve for x

Subtract \( 19x \) from both sides: \( 20x - 19x - 4 = 15 \), which simplifies to \( x - 4 = 15 \). Then add 4 to both sides: \( x = 15 + 4 = 19 \).

Step4: Find PR

Substitute \( x = 19 \) into \( PR = 19x + 15 \): \( PR = 19(19) + 15 \). Calculate \( 19\times19 = 361 \), then \( 361 + 15 = 376 \).

Answer:

376