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Equivalent expressions SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

open parenthesis, 2 x plus 3, close parenthesis, minus, open parenthesis, x minus 7, close parenthesis

Which of the following is equivalent to the given expression?

ExplanationShow

Choice C is correct. Distributing the negative sign to the terms in the second parentheses yields open parenthesis, 2 x plus 3, close parenthesis, minus x, plus 7. This expression can be rewritten as 2 x minus x, plus 3, plus 7. Combining like terms results in x plus 10.

Choice A is incorrect and may result from not distributing the negative sign to the 7. Choice B is incorrect and may result from adding x minus 7 to 2 x plus 3 instead of subtracting x minus 7. Choice D is incorrect and may result from adding the product of 2 x and x to the product of 3 and 7.

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