QuestionAugust 25, 2025

Points A, B, and C are collinear, and B lies between A and C. If AC=48,AB=2x+2 and BC=3x+6 what is BC? BC=square

Points A, B, and C are collinear, and B lies between A and C. If AC=48,AB=2x+2 and BC=3x+6 what is BC? BC=square
Points A, B, and C are collinear, and B lies between A and C. If
AC=48,AB=2x+2 and BC=3x+6 what is BC?
BC=square

Solution
4.5(328 votes)

Answer

30 Explanation 1. Express AC in terms of AB and BC Since points A, B, and C are collinear and B is between A and C, AC = AB + BC. 2. Substitute given expressions Substitute AB = 2x + 2 and BC = 3x + 6 into the equation: 48 = (2x + 2) + (3x + 6). 3. Simplify and solve for x Combine like terms: 48 = 5x + 8. Solve for x: 5x = 40 \Rightarrow x = 8. 4. Calculate BC Substitute x = 8 into BC = 3x + 6: BC = 3(8) + 6 = 24 + 6 = 30.

Explanation

1. Express AC in terms of AB and BC<br /> Since points A, B, and C are collinear and B is between A and C, $AC = AB + BC$.<br />2. Substitute given expressions<br /> Substitute $AB = 2x + 2$ and $BC = 3x + 6$ into the equation: $48 = (2x + 2) + (3x + 6)$.<br />3. Simplify and solve for x<br /> Combine like terms: $48 = 5x + 8$. Solve for $x$: $5x = 40 \Rightarrow x = 8$.<br />4. Calculate BC<br /> Substitute $x = 8$ into $BC = 3x + 6$: $BC = 3(8) + 6 = 24 + 6 = 30$.
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