Given: FG (SEG) bisects BT (SEG)
BO=7x-6
OT=5x+10
Prove: BO=50
I think we need to see the figure, but looking at the given, I think the point FG bisects and intersects BT at point O. Therefore we can say the lengths of segments BO and OT are equal, or
7x - 6 = 5x + 10
7x - 5x = 10 + 6
2x = 16
x = 8
Susbtituting,
BO = 7x - 6
BO = 7(8) - 6
BO = 56 - 6
BO = 50
Hope this helps~ :3