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Nonlinear equations in one variable and systems of equations in two variables SAT question

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

$open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x plus 3, close parenthesis, equals, open parenthesis, x minus 2, close parenthesis, times, open parenthesis, x minus 3, close parenthesis, plus 10$

Which of the following is a solution to the given equation?

ExplanationShow

Choice A is correct. Applying the distributive property on the left- and right-hand sides of the given equation yields $x squared, plus 2 x, plus 3 x, plus 6, equals, x squared, minus 2 x, minus 3 x, plus 6, plus 10$ , or $x squared, plus 5 x, plus 6, equals, x squared, minus 5 x, plus 16$ . Subtracting $x squared$ from and adding $5 x$ to both sides of this equation yields $10 x plus 6, equals 16$ . Subtracting 6 from both sides of this equation and then dividing both sides by 10 yields $x equals 1$ .

Choices B, C, and D are incorrect. Substituting 0, $negative 2$ , or $negative 5$ for x in the given equation will result in a false statement. If $x equals 0$ , the given equation becomes $6 equals 16$ ; if $x equals negative 2$ , the given equation becomes $0 equals 30$ ; and if $x equals negative 5$ , the given equation becomes $6 equals 66$ . Therefore, the values 0, $negative 2$ , and $negative 5$ aren’t solutions to the given equation.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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