What is the positive solution to the equation x = 12x - 4? | SAT Nonlinear equations in one variable and systems of equations in two variables Question, Answer Explained

Question bank / Nonlinear equations in one variable and systems of equations in two variables

Math · Advanced MathMedium

What is the positive solution to the equation $x = \frac{12}{x - 4}$ ?

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Answer: 6

Multiply both sides by $x - 4$ : $x(x - 4) = 12$ , so $x^2 - 4x - 12 = 0$ . Factor: $(x - 6)(x + 2) = 0$ . The solutions are $6$ and $-2$ , so the positive solution is $6$ . Check: $\frac{12}{6 - 4} = 6$ .

Writing $x(x - 4)$ as $x^2 - 4$ gives $x^2 = 16$ and $x = 4$ , which makes the denominator $0$ .

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