Question

point v is on line segment \\(\overline{uw}\\). given \\(vw = x\\), \\(uv = 3x - 1\\), and \\(uw = 5x - 5\\), 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: \( (3x - 1) + x = 5x - 5 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 4x - 1 = 5x - 5 \). Subtract \( 4x \) from both sides: \( -1 = x - 5 \). Add 5 to both sides: \( x = 4 \).

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

Since \( VW = x \) and \( x = 4 \), the length of \( \overline{VW} \) is 4.

Answer:

4