Question

point v lies between points u and w on $overline{uw}$. if uw = 9x - 9, what is uw in units? 2x - 4 4x + 10 o 5 units o 6 units o 30 units o 36 units

Explanation:

Step1: Set up equation based on segment - addition postulate

Since point V lies between U and W, $UV + VW=UW$. So, $(2x - 4)+(4x + 10)=9x - 9$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+4x-4 + 10=6x + 6$. So, $6x+6=9x - 9$.

Step3: Solve for x

Subtract 6x from both sides: $6=9x-6x - 9$, which simplifies to $6 = 3x-9$. Then add 9 to both sides: $6 + 9=3x$, so $15 = 3x$. Divide both sides by 3: $x = 5$.

Step4: Find the length of UW

Substitute $x = 5$ into the expression for UW. $UW=9x-9$. Then $UW=9\times5-9=45 - 9=36$.

Answer:

D. 36 units