Question #52931bfa - SAT Suite Question Bank

ID: 52931bfa

Modded SAT Question Bank by Abdullah Mallik

Which expression is equivalent to $\frac{8 x (x - 7) - 3 (x - 7)}{2 x - 14}$ , where $x greater than 7$ ?

$\frac{x - 7}{5}$
$\frac{8 x - 3}{2}$
$\frac{8 x^{2} - 3 x - 14}{2 x - 14}$
$\frac{8 x^{2} - 3 x - 77}{2 x - 14}$

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Correct Answer: B

Rationale

Choice B is correct. The given expression has a common factor of $2$ in the denominator, so the expression can be rewritten as $\frac{8 x (x - 7) - 3 (x - 7)}{2 (x - 7)}$ . The three terms in this expression have a common factor of $left parenthesis x minus 7 right parenthesis$ . Since it's given that $x greater than 7$ , $x$ can't be equal to $7$ , which means $left parenthesis x minus 7 right parenthesis$ can't be equal to $0$ . Therefore, each term in the expression, $\frac{8 x (x - 7) - 3 (x - 7)}{2 (x - 7)}$ , can be divided by $left parenthesis x minus 7 right parenthesis$ , which gives $\frac{8 x - 3}{2}$ .

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.

Question Difficulty: Medium