Question

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

Explanation:

Step1: Set up equation

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

Step2: Simplify equation

$9x-9 = 2x-4 + 4x + 10$, which simplifies to $9x-9=6x + 6$.

Step3: Solve for x

Subtract $6x$ from both sides: $9x-6x-9=6x-6x + 6$, so $3x-9 = 6$. Add 9 to both sides: $3x=15$, then $x = 5$.

Step4: Find UW

Substitute $x = 5$ into $UW=9x - 9$, so $UW=9\times5-9=45 - 9=36$.

Answer:

36 units