Chapter 1 - Tools of Geometry - 1-3 Measuring Segments - Practice and Problem-Solving Exercises - Page 24: 21

34

Because of the tick marks, we know that PT=TQ. So, we can set their algebraic values equal to each other. That gives $PT=TQ \rightarrow 4x-6=3x+4 \rightarrow x=10$ The question asks for PT, so we substitute 10 back into the equation of PT, which is $4x-6$. $4(10)-6=40-6=34.$