The distance between U and W is 36 units. Option D is the right choice.
A line segment with three points labeled U, V, and W. Point V lies between points U and W. The distance between U and V is labeled 2x-4, and the distance between V and W is labeled 4x+10. The total distance between U and W is labeled 9x-9.
We are asked to find the distance between U and W in units.
We can do this by adding the distances between U and V and between V and W:
UW = UV + VW
UW = (2x-4) + (4x+10)
UW = 6x+6
Since we are given that UW = 9x-9, we can set these two expressions equal to each other and solve for x:
6x+6 = 9x-9
-3x = -15
x = 5
Now that we know x = 5, we can substitute this value into either of the expressions for UW to find the distance between U and W in units:
UW = 6(5) + 6
UW = 30 + 6
UW = 36 units
Option D is the right choice.