Question

q is a point on segment \\( \overline{pr} \\). if \\( pq = x + 14 \\), \\( qr = 20 \\), and \\( pr = 4x - 2 \\), what is \\( pr \\)? 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: \( (x + 14) + 20 = 4x - 2 \).

Step2: Simplify and solve for \( x \)

Simplify the left side: \( x + 34 = 4x - 2 \). Subtract \( x \) from both sides: \( 34 = 3x - 2 \). Add 2 to both sides: \( 36 = 3x \). Divide by 3: \( x = 12 \).

Step3: Find \( PR \)

Substitute \( x = 12 \) into \( PR = 4x - 2 \): \( PR = 4(12) - 2 = 48 - 2 = 46 \).

Answer:

\( 46 \)