Solve: 20x-18<50<36x-16

So this is actually composed o 2 sentances
20x-18<50 AND 50<36x-16
so solve each and find solutions where x is the same in both sentances
20x-18<50
add 18 to both sides
20x<68
divide both sides by 20
x<3 and 2/5
then the second sentance
50<36x-16
add 16 to both sides
66<36x
divide both sides by 36
1 and 5/6<x
so
since it is and, combine
3 and 2/5>x>1 and 5/6 or
17/5>x>11/6

the solution is
S={x|17/5>x>11/6}