Official Guide Explanation:
Problem Solving #97




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Solution and Metadata

Question: 97
Page: 165
Difficulty: 5 (Moderate)
Category 1: Algebra > Solving Quadratic Equations > other
Category 2: Algebra > Solving Equations by Factoring >

Explanation: If the product of two terms is zero, that means that one or both of the terms must be equal to zero. So, if x(2x + 1) = 0, then either x = 0 or (2x + 1) = 0. In other words, x must be 0 or -(1/2). That's not enough information to answer the question, but that's why you're given a second equation. In that case, either (x + (1/2)) = 0 or (2x - 3) = 0, so x must be -(1/2) or (3/2). Since both equations must be true, the only possible x value is the one that appears as a solution in both cases: x= - (1/2), choice (B).

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