Question

point q is on line segment \\(\overline{pr}\\). given \\(qr = 3x\\), \\(pq = x + 6\\), and \\(pr = 5x - 4\\), determine the numerical length of \\(\overline{pq}\\).

Explanation:

Step1: Use segment addition postulate

Since Q is on \(\overline{PR}\), we have \(PQ + QR = PR\). Substituting the given expressions: \((x + 6)+3x = 5x - 4\).

Step2: Simplify and solve for x

Combine like terms: \(4x + 6 = 5x - 4\). Subtract \(4x\) from both sides: \(6 = x - 4\). Add 4 to both sides: \(x = 10\).

Step3: Find length of \(PQ\)

Substitute \(x = 10\) into \(PQ = x + 6\): \(PQ = 10 + 6 = 16\).

Answer:

16