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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.

$p = \frac{k}{4 j + 9}$

The given equation relates the distinct positive numbers $p$ , $k$ , and $j$ . Which equation correctly expresses $4 j + 9$ in terms of $p$ and $k$ ?

ExplanationShow

Choice A is correct. To express $4 j + 9$ in terms of $p$ and $k$ , the given equation must be solved for $4 j + 9$ . Since it's given that $j$ is a positive number, $4 j + 9$ is not equal to zero. Therefore, multiplying both sides of the given equation by $4 j + 9$ yields the equivalent equation $p (4 j + 9) = k$ . Since it's given that $p$ is a positive number, $p$ is not equal to zero. Therefore, dividing each side of the equation $p (4 j + 9) = k$ by $p$ yields the equivalent equation $4 j + 9 = \frac{k}{p}$ .

Choice B is incorrect. This equation is equivalent to $p = \frac{4 j + 9}{k}$ .

Choice C is incorrect. This equation is equivalent to $p = k - 4 j - 9$ .

Choice D is incorrect. This equation is equivalent to $p = k (4 j + 9)$ .

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

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