Question

Find the value of a and TV if U is between T and VTU = 3a - 4, UV = 6a + 2, and TV = 5a + 22

Answer 1

Let us represent this information on a number line.

Since U is the midpoint of TV, it follows that TU=UV.

Hence,

`\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,} \\ (-6)/(2)=(2a)/(2) \\ a=-3 \end{gathered}`

TV = 5a + 22

`\begin{gathered} TV=5(-3)+22 \\ TV=-15+22 \\ TV=7 \end{gathered}`

Thus, a is -3 and TV is 7.