Question

v is the mid - point of uw. if vw = x + 2 and uw = 3x - 1, 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 \(UW = 2VW\).
We know that \(VW=x + 2\) and \(UW=3x−1\), so \(3x−1 = 2(x + 2)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(3x−1=2x + 4\).
Subtract \(2x\) from both sides: \(3x-2x−1=2x-2x + 4\), which gives \(x−1 = 4\).
Add 1 to both sides: \(x=4 + 1=5\).

Step3: Find the value of \(VW\)

Substitute \(x = 5\) into the expression for \(VW\). Since \(VW=x + 2\), then \(VW=5 + 2=7\).

Answer:

7