Answer:
[tex]BC=26[/tex]
Step-by-step explanation:
Start with:
[tex]AB+BC=AC[/tex]
Since [tex]B[/tex] is the midpoint, we also know that:
[tex]AB=BC[/tex]
Knowing this, we can use a system of equations and substitute [tex]AB[/tex] for [tex]BC[/tex] in the equation we started with:
[tex]AB+AB=AC[/tex]
Let's identify our values:
[tex]AB=3x-1\\AC=8x-20[/tex]
Substitute:
[tex]3x-1+3x-1=8x-20[/tex]
Combine like terms:
[tex]6x-2=8x-20[/tex]
Add [tex]20[/tex] to both sides of the equation:
[tex]6x+18=8x[/tex]
Subtract [tex]6x[/tex] from both sides of the equation:
[tex]18=2x[/tex]
Divide by the coefficient of [tex]x[/tex], which is [tex]2.[/tex]
[tex]x=9[/tex]
Substitute [tex]9[/tex] into [tex]3x-1[/tex]
[tex]3(9)-1[/tex]
Solve:
[tex]AB=26[/tex]
Remember that [tex]AB=BC[/tex], thus:
[tex]BC=26[/tex]
