Answer:
BC = 30
Explanation:
Finding x:
Since the points are collinear and B lies between A and C, we know according to the Segment Addition Postulate that the sum of AB and AC equals AC:
AB + BC = AC
Now we can solve for x by substituting 2x + 2 for AB, 3x + 6 for BC, and 48 for AC:
2x + 2 + 3x + 6 = 48
(2x + 3x) + (2 + 6) = 48
(5x + 8 = 48) - 8
(5x = 40) / 5
x = 8
Thus, x = 8.
Finding BC:
Now we can find BC by substituting 8 for x in 3x + 6:
BC = 3(8) + 6
BC = 24 + 6
BC = 30
Therefore, BC = 30.