Given U is the midpoint of TV:
[tex]TU=UV[/tex]
Then,
[tex]8x+11=12x-1[/tex]
Let's find x:
To do it, add 1 to both sides.
[tex]\begin{gathered} 8x+11+1=12x-1+1 \\ 8x+12=12x \end{gathered}[/tex]
Now, subtract 8x from both sides.
[tex]\begin{gathered} 8x+12-8x=12x-8x \\ 12=4x \end{gathered}[/tex]
And divide both sides by 4:
[tex]\begin{gathered} \frac{12}{4}=\frac{4x}{4} \\ 3=x \\ x=3 \end{gathered}[/tex]
Let's find TU:
[tex]\begin{gathered} TU=8x+11 \\ TU=8*3+11 \\ TU=24+11 \\ TU=35 \end{gathered}[/tex]
Let's find UV:
[tex]\begin{gathered} UV=12x-1 \\ UV=12*3-1 \\ UV=36-1 \\ UV=35 \end{gathered}[/tex]
Let's find TV:
[tex]\begin{gathered} TV=TU+UV \\ TV=35+35 \\ TV=70 \end{gathered}[/tex]
In summary:
[tex]\begin{gathered} 8x+11=12-1 \\ x=3 \\ TU=35 \\ UV=35 \\ TV=70 \end{gathered}[/tex]
