Question

point v lies between points u and w on (overline{uw}). if uw = 9x - 9, what is uw in units?

u ---- v ---- w
(2x - 4) (4x + 10)

options:
○ 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 equation

Simplify the right - hand side: \( (2x - 4)+(4x + 10)=2x+4x-4 + 10=6x + 6 \).
The equation becomes \( 9x-9 = 6x + 6 \).
Subtract \( 6x \) from both sides: \( 9x-6x-9=6x-6x + 6 \), which is \( 3x-9 = 6 \).
Add 9 to both sides: \( 3x-9 + 9=6 + 9 \), so \( 3x=15 \).
Divide both sides by 3: \( x=\frac{15}{3}=5 \).

Step3: Find the length of \( UW \)

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

Answer:

36 units