Question

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

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

Combine like terms: \( 9x - 9 = 6x + 6 \).
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 by 3: \( x = 5 \).

Step3: Find \( UW \)

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

Answer:

36 units