Question

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

Explanation:

Step1: Set up equation

Since $UW = UV+VW$ and $UW = 9x - 9$, $UV=2x - 4$, $VW = 4x + 10$, we have $9x-9=(2x - 4)+(4x + 10)$.

Step2: Simplify right - hand side

$(2x - 4)+(4x + 10)=2x-4 + 4x+10=6x + 6$. 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: $3x-9 + 9=6 + 9$, getting $3x=15$. Divide both sides by 3: $x = 5$.

Step4: Find UW

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

Answer:

36 units