Question

question
point w is on line segment (overline{vx}). given (vw = 4x - 7), (vx = 5x + 1), and (wx = 3x), determine the numerical length of (overline{vw}).

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Explanation:

Step1: Use segment addition postulate

Since \( W \) is on \( \overline{VX} \), we have \( VW + WX = VX \). Substitute the given expressions: \( (4x - 7) + 3x = 5x + 1 \).

Step2: Solve for \( x \)

Combine like terms: \( 7x - 7 = 5x + 1 \). Subtract \( 5x \) from both sides: \( 2x - 7 = 1 \). Add 7 to both sides: \( 2x = 8 \). Divide by 2: \( x = 4 \).

Step3: Find \( VW \)

Substitute \( x = 4 \) into \( VW = 4x - 7 \): \( VW = 4(4) - 7 = 16 - 7 = 9 \).

Answer:

\( 9 \)