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Algebra / Linear equations in one variable Difficulty: Hard

If x-57=x-59, the value of x-5 is between which of the following pairs of values?

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Explanation

Choice B is correct. Multiplying both sides of the given equation by (7)(9), or 63, yields (63)x-57=(63)x-59, or 9(x-5)=7(x-5). Subtracting 7(x-5) from both sides of this equation yields 2(x-5)=0. Dividing both sides of this equation by 2 yields x-5=0. Therefore, if x-57=x-59, then the value of x-5 is 0. It follows that of the given choices, the value of x-5 is between -3 and 3.

Choice A 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.