Question

v is the midpoint of $overline{uw}$. if $uv = 7x$ and $vw = 10x - 4$, what is $vw?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(V\) is the mid - point of \(\overline{UW}\), then \(UV = VW\). So, \(7x=10x - 4\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(0 = 10x-7x - 4\), which simplifies to \(0 = 3x - 4\). Then add 4 to both sides: \(3x=4\), and \(x=\frac{4}{3}\).

Step3: Find \(VW\)

Substitute \(x = \frac{4}{3}\) into the expression for \(VW\). \(VW=10x - 4=10\times\frac{4}{3}-4=\frac{40}{3}-4=\frac{40}{3}-\frac{12}{3}=\frac{40 - 12}{3}=\frac{28}{3}=9\frac{1}{3}\).

Answer:

\(9\frac{1}{3}\)