Question

point v lies between points u and w on \overline{uw}.
if uw = 9x - 9, what is uw in units?
5 units
6 units
30 units
36 units

Explanation:

Step1: Use the segment addition postulate

Since \(V\) lies between \(U\) and \(W\), we have \(UV + VW=UW\).
Given \(UV = 2x - 4\), \(VW=4x + 10\), and \(UW = 9x-9\).
Substitute into the equation: \((2x - 4)+(4x + 10)=9x - 9\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x-4 + 4x+10=(2x + 4x)+(-4 + 10)=6x + 6\).
So the equation becomes \(6x+6 = 9x-9\).

Step3: Solve for \(x\)

Subtract \(6x\) from both sides: \(6x+6-6x=9x - 9-6x\), which gives \(6 = 3x-9\).
Add \(9\) to both sides: \(6 + 9=3x-9 + 9\), so \(15 = 3x\).
Divide both sides by \(3\): \(x=\frac{15}{3}=5\).

Step4: Find the length of \(UW\)

Substitute \(x = 5\) into the formula for \(UW\): \(UW=9x-9\).
\(UW=9\times5-9\).
First, calculate \(9\times5 = 45\), then \(45-9=36\).

Answer:

\(36\) units