Question

q is a point on segment \\( \overline{pr} \\). if \\( pq = x + 8 \\), \\( qr = 7x \\), and \\( pr = 17x - 19 \\), what is \\( pq \\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

Since \( Q \) is on \( \overline{PR} \), we have \( PQ + QR = PR \). Substituting the given expressions: \( (x + 8) + 7x = 17x - 19 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 8x + 8 = 17x - 19 \). Subtract \( 8x \) from both sides: \( 8 = 9x - 19 \). Add 19 to both sides: \( 27 = 9x \). Divide by 9: \( x = 3 \).

Step3: Find \( PQ \)

Substitute \( x = 3 \) into \( PQ = x + 8 \): \( PQ = 3 + 8 = 11 \).

Answer:

11