If U is the midpoint of TV, then:
TU = UV
[tex]\begin{gathered} 4x+1=5x-8 \\ \text{Solving for x:} \\ \text{Subtract 4x from both sides:} \\ 1=5x-8-4x \\ 1=x-8 \\ \text{add 8 to both sides:} \\ 1+8=x \\ x=9 \end{gathered}[/tex]Since UV = 5x - 8, replace the value of x into that equation:
[tex]UV=5(9)-8=45-8=37[/tex]