Question

point v lies between points u and w on \\(\overline{uw}\\). if \\(uw = 9x - 9\\), what is \\(uw\\) in units? \\(\bigcirc\\) 5 units \\(\bigcirc\\) 6 units \\(\bigcirc\\) 30 units \\(\bigcirc\\) 36 units (with a line segment diagram: u---v---w, segment uv is \\(2x - 4\\), segment vw is \\(4x + 10\\))

Explanation:

Step1: Use segment addition postulate

Since \( V \) is 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 \( 9x-9 = 6x + 6 \).

Step3: Solve for \( x \)

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

Step4: Find \( UW \)

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

Answer:

36 units