Question

point v lies between points u and w on uw.
if uw = 9x - 9, what is uw in units?
2x - 4
4x + 10
5 units
6 units
30 units
36 units

Explanation:

Step1: Apply the segment addition postulate

Since \(V\) lies between \(U\) and \(W\), \(UW = UV+VW\).
We know \(UV = 2x - 4\), \(VW=4x + 10\), and \(UW=9x - 9\).
So, \(2x-4+(4x + 10)=9x - 9\).

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \(x\)

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

Step4: Find the length of \(UW\)

Substitute \(x = 5\) into the formula for \(UW\) (\(UW=9x - 9\)).
\(UW=9\times5-9\).
\(UW = 45-9\).
\(UW=36\).

Answer:

36 units