Solve for x (2pi)/x=6pi

$\frac{2 π}{x} = 6 π$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Step 2

Multiply each term in $\frac{2 π}{x} = 6 π$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{2 π}{x} = 6 π$ by $x$ .

$\frac{2 π}{x} x = 6 π x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{2 π}{x} x = 6 π x$

Rewrite the expression.

$2 π = 6 π x$

Step 3

Solve the equation.

Rewrite the equation as $6 π x = 2 π$ .

$6 π x = 2 π$

Divide each term in $6 π x = 2 π$ by $6 π$ and simplify.

Divide each term in $6 π x = 2 π$ by $6 π$ .

$\frac{6 π x}{6 π} = \frac{2 π}{6 π}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 π x}{6 π} = \frac{2 π}{6 π}$

Rewrite the expression.

$\frac{π x}{π} = \frac{2 π}{6 π}$

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{π x}{π} = \frac{2 π}{6 π}$

Divide $x$ by $1$ .

$x = \frac{2 π}{6 π}$

Simplify the right side.

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2 π$ .

$x = \frac{2 (π)}{6 π}$

Cancel the common factors.

Factor $2$ out of $6 π$ .

$x = \frac{2 (π)}{2 (3 π)}$

Cancel the common factor.

$x = \frac{2 π}{2 (3 π)}$

Rewrite the expression.

$x = \frac{π}{3 π}$

Cancel the common factor of $π$ .

Cancel the common factor.

$x = \frac{π}{3 π}$

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}$

Solve for x (2pi)/x=6pi

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