Question

question
point v is on line segment uw. given uv = 6, uw = 5x, and vw = 4x - 1, determine the numerical length of vw.
answer attempt 1 out of 3
vw =

Explanation:

Step1: Use segment addition postulate

Since point \( V \) is on line segment \( UW \), we have \( UW = UV + VW \). Substituting the given values, we get \( 5x = 6 + (4x - 1) \).

Step2: Solve for \( x \)

Simplify the right - hand side of the equation: \( 5x=6 + 4x-1\). Combine like terms: \( 5x=4x + 5\). Subtract \( 4x \) from both sides: \( 5x-4x=4x + 5-4x\), so \( x = 5 \).

Step3: Find the length of \( VW \)

We know that \( VW = 4x-1 \). Substitute \( x = 5 \) into the expression for \( VW \): \( VW=4\times5 - 1\). Calculate \( 4\times5=20 \), then \( 20 - 1 = 19 \).

Answer:

\( 19 \)