B is the midpoint of AC.
Then AB=BC and AB + BC=AC.
Then we can write:
[tex]\begin{gathered} AB+BC=AC \\ (3x-1)+(3x-1)=8x-20 \\ 6x-2=8x-20 \\ -2+20=8x-6x \\ 2x=18 \\ x=\frac{18}{2} \\ x=9 \end{gathered}[/tex]Then BC is:
[tex]BC=3x-1=3\cdot9-1=27-1=26[/tex]Answer: BC = 26
