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Advanced Math
/ Nonlinear equations in one variable and systems of equations in two variables
Difficulty: Hard
What is the sum of the solutions to the given equation?
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Explanation
Choice D is correct. By the definition of absolute value, if , then or . Subtracting from both sides of the equation yields . Dividing both sides of this equation by yields . Subtracting from both sides of the equation yields . Dividing both sides of this equation by yields . Therefore, the solutions to the given equation are and , and it follows that the sum of the solutions to the given equation is , or .
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect. This is a solution, not the sum of the solutions, to the given equation.
Choice C is incorrect and may result from conceptual or calculation errors.