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 segment addition postulate

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

Step2: Simplify the right - hand side

\((2x - 4)+(4x + 10)=2x-4 + 4x+10=6x + 6\).
The equation becomes \(9x−9=6x + 6\).

Step3: Solve for \(x\)

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

Step4: Find \(UW\)

Substitute \(x = 5\) into \(UW=9x−9\).
\(UW=9\times5−9=45−9=36\) units.

Answer:

D. 36 units