Question

Using the following image, solve the problems below given that U is the midpoint of TV

Answer 1

Given U is the midpoint of TV:

`TU=UV`

Then,

`8x+11=12x-1`

Let's find x:

To do it, add 1 to both sides.

`\begin{gathered} 8x+11+1=12x-1+1 \\ 8x+12=12x \end{gathered}`

Now, subtract 8x from both sides.

`\begin{gathered} 8x+12-8x=12x-8x \\ 12=4x \end{gathered}`

And divide both sides by 4:

`\begin{gathered} (12)/(4)=(4x)/(4) \\ 3=x \\ x=3 \end{gathered}`

Let's find TU:

`\begin{gathered} TU=8x+11 \\ TU=8*3+11 \\ TU=24+11 \\ TU=35 \end{gathered}`

Let's find UV:

`\begin{gathered} UV=12x-1 \\ UV=12*3-1 \\ UV=36-1 \\ UV=35 \end{gathered}`

Let's find TV:

`\begin{gathered} TV=TU+UV \\ TV=35+35 \\ TV=70 \end{gathered}`

In summary:

`\begin{gathered} 8x+11=12-1 \\ x=3 \\ TU=35 \\ UV=35 \\ TV=70 \end{gathered}`