Let us represent this information on a number line.
Since U is the midpoint of TV, it follows that TU=UV.
Hence,
[tex]\begin{gathered} 3a-4=5a+2 \\ \text{Collecting like terms} \\ 3a-4-3a-2=5a+2-3a-2 \\ -4-2=2a \\ -6=2a \\ \text{Dividing both sides by 2,} \\ \frac{-6}{2}=\frac{2a}{2} \\ a=-3 \end{gathered}[/tex]TV = 5a + 22
[tex]\begin{gathered} TV=5(-3)+22 \\ TV=-15+22 \\ TV=7 \end{gathered}[/tex]Thus, a is -3 and TV is 7.
