Given a line segment that contains the points A,B, & C in order, and given that B is the midpoint of AC, if AB = 2x - 5, and BC = x + 7, find x.
Question
Given a line segment that contains the points A,B, & C in order, and given that B is the midpoint of AC, if AB = 2x - 5, and BC = x + 7, find x.
Solution
Since B is the midpoint of AC, this means that AB = BC.
So, we can set the expressions for AB and BC equal to each other and solve for x:
2x - 5 = x + 7
To solve for x, first subtract x from both sides of the equation:
2x - x = 7 + 5
This simplifies to:
x = 12
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