Question

Point V lies between points U and W on Line segment U W.

A line has points U, V, W. The length between U V is 2x - 4. The length between V W is 4x + 10.
If UW = 9x - 9, what is UW in units?

a) 5 units
b) 6 units
c) 30 units
d) 36 units

Answer 1

The length of Line segment UW when calculated by the given expressions and combined like terms, after finding the value of x to be 5, is found to be 36 units which is option (d).

Step-by-step explanation:

To solve for the length of Line segment UW, we must recognize that the sum of the lengths of segments UV and VW is equal to the length of segment UW. The problem gives us the following expressions for the lengths of these segments:

Since UW is the entire segment, adding the lengths of UV and VW should match the expression given for UW:

(2x - 4) + (4x + 10) = 9x - 9

By combining like terms, we get:

6x + 6 = 9x - 9

Next, we can solve for x:

6 + 9 = 9x - 6x

15 = 3x

x = 5

Now that we have the value of x, we can substitute it back into the expression for UW:

UW = 9(5) - 9

UW = 45 - 9

UW = 36 units

Therefore, the length of segment UW in units is option (d) 36 units.