Question

v is the midpoint of $overline{uw}$. if $uv = x + 3$ and $vw = 4x$, what is $uv?
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 we set up the equation \(x + 3=4x\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation \(x + 3=4x\). We get \(3=4x - x\), which simplifies to \(3 = 3x\). Then divide both sides by 3, so \(x = 1\).

Step3: Find the value of \(UV\)

Substitute \(x = 1\) into the expression for \(UV\). Since \(UV=x + 3\), then \(UV=1+3=4\).

Answer:

4