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 \( W \), \( UV+VW = UW \).
Substitute \( UV = 2x - 4 \), \( VW = 4x + 10 \), and \( UW=9x - 9 \) into the equation:
\( (2x - 4)+(4x + 10)=9x - 9 \)

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \( x \)

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

Step4: Find the length of \( UW \)

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

Answer:

36 units