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Algebra Difficulty: Hard

If $\frac{x + 6}{3} = \frac{x + 6}{13}$ , the value of $x plus 6$ 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 $left parenthesis 3 right parenthesis left parenthesis 13 right parenthesis$ , or $39$ , yields $(39) (\frac{x + 6}{3}) = (39) (\frac{x + 6}{13})$ , or $13 (x + 6) = 3 (x + 6)$ . Subtracting $3 left parenthesis x plus 6 right parenthesis$ from both sides of this equation yields $10 (x + 6) = 0$ . Dividing both sides of this equation by $10$ yields $x + 6 = 0$ . Therefore, if $\frac{x + 6}{3} = \frac{x + 6}{13}$ , then the value of $x plus 6$ is $0$ . It follows that of the given choices, the value of $x plus 6$ is between $negative 2$ and $2$ .

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.