Question

10 in the diagram, m is the midpoint of \\(\overline{vw}\\). find vm. algebraic setup: rectangle vm = rectangle (diagram: points v, m, w on a line; segment vm labeled \\(4x - 1\\), segment mw labeled \\(3x + 3\\))

Explanation:

Step1: Set VM = MW (Midpoint Definition)

Since \( M \) is the midpoint of \( \overline{VW} \), \( VM = MW \). Given \( VM = 4x - 1 \) and \( MW = 3x + 3 \), we set up the equation:
\( 4x - 1 = 3x + 3 \)

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\( 4x - 3x - 1 = 3x - 3x + 3 \)
\( x - 1 = 3 \)

Add 1 to both sides:
\( x - 1 + 1 = 3 + 1 \)
\( x = 4 \)

Step3: Find \( VM \)

Substitute \( x = 4 \) into \( VM = 4x - 1 \):
\( VM = 4(4) - 1 \)
\( VM = 16 - 1 \)
\( VM = 15 \)

Answer:

\( 15 \)