If M is the midpoint of PQ, then PM and MQ are equal.
As PM and MQ are given , equal them to each other to solve for x.
7x+8=5x+20
Subtract 5x on both sides to get 2x+8=20
Subtract 8 on both sides to get 2x=12
divide by 2 on both sides to get x=6
Use the value of x=6 and plug it into the equations for PM and MQ to find their value.
PM=7x+8
=7(6) 8 =42 + 8 = 50
(you can already tell MQ is also 50 as PM and MQ are equal, but we still solve for MQ just for the fun of it)
MQ=5x + 20
=5(6) +20=30+20=50
PM=50
MQ=50
PQ= PM + MQ= 50 + 50 = 100
Have a great night.