point v lies between points u and w on $overline{uw}$. if uw = 9x - 9, what is uw in units? 5 units 6 units…

Explanation:

Step1: Use segment - addition postulate

Since point V lies between U and W on $\overline{UW}$, we have $UW=UV + VW$. So, $9x−9=(2x - 4)+(4x + 10)$.

Step2: Simplify the right - hand side of the equation

Combine like terms on the right - hand side: $(2x - 4)+(4x + 10)=2x+4x-4 + 10=6x + 6$. So the equation becomes $9x−9=6x + 6$.

Step3: Solve for x

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

Step4: Find the length of UW

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

Answer:

36 units