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

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Grade 7

Divide fractions

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

Understand and Identify: Understand the equation and identify what is being asked. $\newline$ We need to find the value of $x$ in the equation $x = \frac{12}{\frac{1}{3}x}$ . This is a simple algebraic equation where $x$ is present on both sides of the equation.
Simplify the Equation: Simplify the equation. $\newline$ 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. $\newline$ x \cdot (\(1/ $3$ )x = \frac{ $12$ }{( $1$ )/( $3$ )x} \cdot ( $1$ / $3$ )x
Multiply Right Side: Perform the multiplication on the right side of the equation. $\newline$ $(12)/((1)/(3)x) \times (1/3)x$ simplifies to $12$ because the $(1/3)x$ in the denominator and the $(1/3)x$ in the numerator cancel each other out. $\newline$ $x \times (1/3)x = 12$
Multiply Left Side: Perform the multiplication on the left side of the equation. $\newline$ $x \times (\frac{1}{3})x$ simplifies to $(\frac{1}{3})x^2$ because we are multiplying $x$ by $(\frac{1}{3})x$ . $\newline$ $(\frac{1}{3})x^2 = 12$
Eliminate Fraction: Multiply both sides of the equation by $3$ to eliminate the fraction on the left side. $3 \times \left(\frac{1}{3}\right)x^2 = 12 \times 3$ $x^2 = 36$
Take Square Root: Take the square root of both sides to solve for $x$ . $\sqrt{x^2} = \sqrt{36}$ $x = \pm6$
Check Solution: Check the solution in the original equation. $\newline$ We have two possible solutions for x: $6$ and $-6$ . We need to check both in the original equation to see if they work. $\newline$ For $x = 6$ : $\newline$ $6 = \frac{12}{\left(\frac{1}{3}\right)6}$ $\newline$ $6 = \frac{12}{1/18}$ $\newline$ $6 = 12 \times \left(\frac{18}{1}\right)$ $\newline$ $6 = 216$ (This is incorrect, so $x = 6$ is not a solution.)