We want to find the length of PT.
From the figure [given T is midpoint of PQ], we can write:
[tex]PT+TQ=PQ[/tex]
We are given expressions for PT and TQ, we know they are equal. Thus, we can equate them and solve for x.
[tex]\begin{gathered} PT=TQ \\ 3x+8=5x-6 \\ 8+6=5x-3x \\ 14=2x \\ x=\frac{14}{2} \\ x=7 \end{gathered}[/tex]
The length of PT is "3x + 8". We know x = 7, so we can figure out the length of PT:
[tex]\begin{gathered} PT=3x+8 \\ PT=3(7)+8 \\ PT=21+8 \\ PT=29 \end{gathered}[/tex]
