x=(12)/((1)/(3)x)

Question

x=(12)/((1)/(3)x)

Bytelearn · Accepted Answer

Understand and Identify: Understand the equation and identify what is being asked. We need to find the value of x in the equation x = (12)/((1)/(3)x). This is a simple algebraic equation where x is present on both sides of the equation.Simplify the Equation: Simplify the equation. To solve for x, we need to get rid of the fraction on the right side of the equation. We can do this by multiplying both sides of the equation by (1/3)x to eliminate the denominator. x * (1/3)x = (12)/((1)/(3)x) * (1/3)xMultiply Right Side: Perform the multiplication on the right side of the equation. (12)/((1)/(3)x) * (1/3)x simplifies to 12 because the (1/3)x in the denominator and the (1/3)x in the numerator cancel each other out. x * (1/3)x = 12Multiply Left Side: Perform the multiplication on the left side of the equation. x * (1/3)x simplifies to (1/3)x^2 because we are multiplying x by (1/3)x. (1/3)x^2 = 12Eliminate Fraction: Multiply both sides of the equation by 3 to eliminate the fraction on the left side. 3 * (1/3)x^2 = 12 * 3 x^2 = 36Take Square Root: Take the square root of both sides to solve for x. √x^2 = √36 x = ±6Check Solution: Check the solution in the original equation. We have two possible solutions for x: 6 and -6. We need to check both in the original equation to see if they work. For x = 6: 6 = (12)/((1)/(3)*6) 6 = (12)/(1/18) 6 = 12 * (18/1) 6 = 216 (This is incorrect, so x = 6 is not a solution.)

$x=\frac{12}{\frac{1}{3} x}$

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$x=\frac{12}{\frac{1}{3} x}$