Question

14 if uw = 6x - 35, use the segment addition postulate to find vw.
diagram: points u, v, w on a line; uv segment labeled 19, vw segment labeled 4x - 20
options:
a ( vw = 67 )
b ( vw = 17 )
c ( vw = 48 )
d ( vw = 26 )

Explanation:

Step1: Apply Segment Addition Postulate

The Segment Addition Postulate states that \( UW = UV + VW \). From the diagram, \( UV = 19 \) and \( VW = 4x - 20 \), and \( UW = 6x - 35 \). So we set up the equation:
\( 6x - 35 = 19 + (4x - 20) \)

Step2: Solve for \( x \)

Simplify the right - hand side of the equation: \( 19+(4x - 20)=4x - 1 \)
So the equation becomes \( 6x - 35 = 4x - 1 \)
Subtract \( 4x \) from both sides: \( 6x-4x - 35=4x - 4x-1 \), which gives \( 2x - 35=-1 \)
Add 35 to both sides: \( 2x-35 + 35=-1 + 35 \), so \( 2x = 34 \)
Divide both sides by 2: \( x=\frac{34}{2}=17 \)

Step3: Find \( VW \)

We know that \( VW = 4x - 20 \). Substitute \( x = 17 \) into the expression for \( VW \):
\( VW=4\times17-20 \)
First, calculate \( 4\times17 = 68 \)
Then, \( 68-20 = 48 \)

Answer:

C. \( VW = 48 \)