Can someone me with number 5? it's on a take home quiz and i'm really confused!

ac=9, cd=2x-6, ab=2, bd = 3x-7


bc = ac - ab = 9 - 2 = 7

bd = bc + cd
3x - 7 = 7 + 2x - 6
3x - 7 = 2x + 1 
3x - 2x = 1 + 7
x = 8

We have two pairs of segments that each add up to the whole length of the line: ac+cd and ab+bd. since both pairs give the same full line, they must be equal. 

we can show this with an equation:

then substitute given values:

combine like terms:


isolate terms with :

and simplify: