Question

point q is on line segment \\( \overline { p r } \\). given \\( p r = 2 x \\), \\( p q = 5 x - 4 \\), and \\( q r = x \\), determine the numerical length of \\( \overline { p r } \\).

Explanation:

Step1: Use segment addition postulate

Since \(Q\) is on \(\overline{PR}\), \(PQ + QR=PR\).
Substitute the given expressions: \(5x - 4+x = 2x\).

Step2: Simplify the left - hand side

Combine like terms: \(6x-4 = 2x\).

Step3: Solve for \(x\)

Subtract \(2x\) from both sides: \(6x-2x - 4=2x-2x\), which gives \(4x-4 = 0\).
Add \(4\) to both sides: \(4x-4 + 4=0 + 4\), so \(4x=4\).
Divide both sides by \(4\): \(x = 1\).

Step4: Find the length of \(PR\)

Since \(PR = 2x\) and \(x = 1\), then \(PR=2\times1\).

Answer:

\(2\)