Solve for x (2pi)/x=3pi

$\frac{2 π}{x} = 3 π$

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.

$x$

Multiply each term in $\frac{2 π}{x} = 3 π$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{2 π}{x} = 3 π$ by $x$ .

$\frac{2 π}{x} x = 3 π x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{2 π}{x} x = 3 π x$

Rewrite the expression.

$2 π = 3 π x$

Solve the equation.

Rewrite the equation as $3 π x = 2 π$ .

$3 π x = 2 π$

Divide each term in $3 π x = 2 π$ by $3 π$ and simplify.

Divide each term in $3 π x = 2 π$ by $3 π$ .

$\frac{3 π x}{3 π} = \frac{2 π}{3 π}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 π x}{3 π} = \frac{2 π}{3 π}$

Rewrite the expression.

$\frac{π x}{π} = \frac{2 π}{3 π}$

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{π x}{π} = \frac{2 π}{3 π}$

Divide $x$ by $1$ .

$x = \frac{2 π}{3 π}$

Simplify the right side.

Cancel the common factor of $π$ .

Cancel the common factor.

$x = \frac{2 π}{3 π}$

Rewrite the expression.

$x = \frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$