CF + FE = CE. Since F is the midpoint, then CF = FE, So, CF + CF = CE ⇒ 2CF = CE
Now, set up the proportion:
[tex]\frac{BF}{CF} = \frac{AE}{CE}[/tex]
[tex]\frac{23}{CF} = \frac{5x - 4}{2CF}[/tex] substituted known values
23(2CF) = CF(5x - 4) cross multiplied
23(2) = 5x - 4 divided both sides by CF
46 = 5x - 4 simplified
50 = 5x added 4 to both sides
10 = x divided both sides by 5
Answer: 10
