Question

10 in the diagram, m is the midpoint of $overline{vw}$. find vm. algebraic setup: blank vm = blank v---m---w with vm labeled $4x - 1$ and mw labeled $3x + 3$

Explanation:

Step1: Set VM = MW (Midpoint Definition)

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

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 4x - 3x - 1 = 3x - 3x + 3 \), which simplifies to \( x - 1 = 3 \). Then add 1 to both sides: \( x - 1 + 1 = 3 + 1 \), so \( x = 4 \).

Step3: Find \( VM \)

Substitute \( x = 4 \) into the expression for \( VM \) (which is \( 4x - 1 \)): \( 4(4) - 1 = 16 - 1 = 15 \).

Answer:

\( 15 \)