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Advanced Math / Equivalent expressions Difficulty: Medium

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

Which of the following is equivalent to the given expression?

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Explanation

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.