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2005 AMC 10A Problem 3

Problem 3 of 25EasierAlgebra

The equations 2x+7=32x + 7 = 3 and bx−10=−2bx - 10 = -2 have the same solution x.x. What is the value of b?b?

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Solution

From 2x+7=32x + 7 = 3 we get x=−2.x = -2. Substituting, −2b−10=−2,-2b - 10 = -2, so −2b=8-2b = 8 and b=−4.b = -4. Thus, the correct answer is B.

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Concepts: linear equation · substitution

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.