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Advanced Math / Equivalent expressions Difficulty: Easy

The expression $2 x squared, plus a, x$ is equivalent to $x times, open parenthesis, 2 x, plus 7, close parenthesis$ for some constant a. What is the value of a ?

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Explanation

Choice D is correct. It’s given that $2 x squared, plus a, x$ is equivalent to $x times, open parenthesis, 2 x plus 7, close parenthesis$ for some constant a. Distributing the x over each term in the parentheses gives $2 x squared, plus 7 x$ , which is in the same form as the first given expression, $2 x squared, plus a, x$ . The coefficient of the second term in $2 x squared, plus 7 x$ is 7. Therefore, the value of a is 7.

Choice A is incorrect. If the value of a were 2, then $2 x squared, plus a, x$ would be equivalent to $2 x squared, plus 2 x$ , which isn’t equivalent to $x times, open parenthesis, 2 x plus 7, close parenthesis$ . Choice B is incorrect. If the value of a were 3, then $2 x squared, plus a, x$ would be equivalent to $2 x squared, plus 3 x$ , which isn’t equivalent to $x times, open parenthesis, 2 x plus 7, close parenthesis$ . Choice C is incorrect. If the value of a were 4, then $2 x squared, plus a, x$ would be equivalent to $2 x squared, plus 4 x$ , which isn’t equivalent to $x times, open parenthesis, 2 x plus 7, close parenthesis$ .