Answer:
43
Step-by-step explanation:
[tex] AB = x + 6 [/tex]
[tex] AC = 3x - 31 [/tex]
Since AB = BC, therefore, [tex] BC = \frac{1}{2}3x - 31 [/tex].
Thus,
[tex] x + 6 = \frac{1}{2}3x - 31 [/tex]
Solve for x
[tex] 2(x + 6) = (\frac{1}{2}3x - 31)2 [/tex] (multiplying both sides by 2)
[tex] 2x + 12 = 3x - 31 [/tex]
Collect like terms
[tex] 2x - 3x = - 12 - 31 [/tex]
[tex] -x = -43[/tex]
Divide both sides by -1
[tex] x = 43[/tex]
