Question

Point V is on the line segment UW. Given VW= x + 7, UW= 3x -9, and UV=8, determine the length of UW

Answer 1

We have that the point V is on the line segment UW. This represents a situation similar to this:

In this case, we get that:

`UV+VW=UW`

Which means that:

`8+x+7=3x-9`

Clearing out the variable x, we obtain that:

`\begin{gathered} 15+x=3x-9 \\ 15+9=3x-x \\ 24=2x \\ (24)/(2)=x \\ 12=x \end{gathered}`

Now, we just have to replace the value of x on the equation of UW, and we obtain:

`\begin{gathered} UW=3x-9 \\ =3(12)-9 \\ =36-9 \\ =27 \end{gathered}`

This means that the value of UW is 27.