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Advanced Math / Equivalent expressions Difficulty: Medium

$open parenthesis, one-half x, plus 3, close parenthesis, minus, open parenthesis, two-thirds x, minus 5, close parenthesis$

Which of the following is equivalent to the expression above?

A. $negative one sixth x, plus 8$

B. $negative one sixth x, minus 2$

C. $negative one-third x squared, plus one-half x, plus 15$

D. $negative one-third x squared, minus nine halves x, minus 15$

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Explanation

Choice A is correct. By distributing the minus sign through the expression $two thirds x minus 5$ , the given expression can be rewritten as $open parenthesis, one half x plus 3, close parenthesis, minus two thirds x, plus 5$ , which is equivalent to $one half x, minus two thirds x, plus 3, plus 5$ . Combining like terms gives $open parenthesis, one half minus two thirds, close parenthesis, times x, plus, open parenthesis, 3 plus 5, close parenthesis$ , or $negative one sixth x plus 8$ .

Choice B is incorrect and may be the result of failing to distribute the minus sign appropriately through the second term and simplifying the expression $one half x, plus 3, minus two thirds x, minus 5$ . Choice C is incorrect and may be the result of multiplying the expressions $one half x plus 3$ and $negative two thirds x plus 5$ . Choice D is incorrect and may be the result of multiplying the expressions $one half x plus 3$ and $negative two thirds x minus 5$ .