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Algebra / Linear equations in one variable Difficulty: Hard

How many solutions does the equation 12x-3=-3x+12 have?

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Explanation

Choice A is correct. Distributing 12 on the left-hand side and -3 on the right-hand side of the given equation yields 12x-36=-3x-36. Adding 3 x to each side of this equation yields 15x-36=-36. Adding 36 to each side of this equation yields 15 x = 0 . Dividing each side of this equation by 15 yields x = 0 . This means that 0 is the only solution to the given equation. Therefore, the given equation has exactly one solution.

Choice B is incorrect and may result from conceptual or calculation errors. 

Choice C is incorrect and may result from conceptual or calculation errors. 

Choice D is incorrect and may result from conceptual or calculation errors.