Answer: x = 8
Work Shown:
I think your teacher meant to say "CA is the perpendicular bisector of BD"
BD is cut in half getting the two equal smaller pieces BC and CD
BC = CD
5x-11 = 3x+5
5x-3x = 5+11
2x = 16
x = 16/2
x = 8
As a check,
BC = 5x-11 = 5*8-11 = 40-11 = 29
CD = 3x+5 = 3*8+5 = 24+5 = 29
Both BC and CD are 29 units long, so this confirms our answer.