Question

point v is on line segment \\(\overline{uw}\\). given \\(vw = 5x - 4\\), \\(uv = 2x\\), and \\(uw = 5x\\), determine the numerical length of \\(\overline{vw}\\).

Explanation:

Step1: Apply segment addition postulate

Since V is on \( \overline{UW} \), we have \( UV + VW = UW \). Substituting the given expressions: \( 2x + (5x - 4) = 5x \).

Step2: Solve for x

Simplify the left side: \( 2x + 5x - 4 = 5x \) → \( 7x - 4 = 5x \). Subtract \( 5x \) from both sides: \( 2x - 4 = 0 \). Add 4 to both sides: \( 2x = 4 \). Divide by 2: \( x = 2 \).

Step3: Find length of \( \overline{VW} \)

Substitute \( x = 2 \) into \( VW = 5x - 4 \): \( 5(2) - 4 = 10 - 4 = 6 \).

Answer:

6