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Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Medium

d-30d+30-7=-7

What is a solution to the given equation?

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Explanation

The correct answer is either -30 or 30 . Adding 7 to each side of the given equation yields d-30d+30=0. Since a product of two factors is equal to 0 if and only if at least one of the factors is 0 , either d - 30 = 0 or d + 30 = 0 . Adding 30 to each side of the equation d - 30 = 0 yields d = 30 . Subtracting 30 from each side of the equation d + 30 = 0 yields d = -30 . Therefore, the solutions to the given equation are -30 and 30 . Note that -30 and 30 are examples of ways to enter a correct answer.