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 2 x minus 4. The length between V W is 4 x + 10.
If UW = 9x – 9, what is UW in units?
5 units
6 units
30 units
36 units
To find UW in terms of x, we can add the lengths UV and VW together: (2x - 4) + (4x + 10) = 6x + 6.
Now, we know UW is equal to 9x - 9.
Setting these two expressions equal to each other, we get 6x + 6 = 9x - 9.
Subtracting 6x from both sides, we get 6 = 3x - 9.
Adding 9 to both sides, we get 15 = 3x.
Dividing both sides by 3, we get x = 5.
Now we can substitute x = 5 into the expression for UW: UW = 9(5) - 9 = 45 - 9 = 36.
Therefore, UW is 36 units.
To find the length UW, we need to add the lengths UV and VW.
Given:
Length UV = 2x - 4
Length VW = 4x + 10
Length UW = 9x - 9
To find the value of x, we can equate the lengths UV and VW and solve for x:
2x - 4 = 4x + 10
-4x - 2x = 10 + 4
-6x = 14
x = -14/6
x = -7/3
Now we can substitute the value of x into the expression for UW:
Length UW = 9(-7/3) - 9
Length UW = -63/3 - 9
Length UW = -21 - 9
Length UW = -30
Since we're dealing with lengths, UW should be a positive value. Therefore, the length UW in units is 30 units. So the correct answer is option C: 30 units.