Solve 12sqrt{2}=2/sqrt{3}x

$$12 \sqrt { 2 } = \frac { 2 } { \sqrt { 3 } } x$$

Solve for x

$$x=6\sqrt{6}\approx 14.696938457$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$12\sqrt{2}=\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}x$$

The square of \sqrt{3} is 3.

$$12\sqrt{2}=\frac{2\sqrt{3}}{3}x$$

Express \frac{2\sqrt{3}}{3}x as a single fraction.

$$12\sqrt{2}=\frac{2\sqrt{3}x}{3}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{2\sqrt{3}x}{3}=12\sqrt{2}$$

Multiply both sides of the equation by 3.

$$2\sqrt{3}x=36\sqrt{2}$$

Divide both sides by 2\sqrt{3}.

$$\frac{2\sqrt{3}x}{2\sqrt{3}}=\frac{36\sqrt{2}}{2\sqrt{3}}$$

Dividing by 2\sqrt{3} undoes the multiplication by 2\sqrt{3}.

$$x=\frac{36\sqrt{2}}{2\sqrt{3}}$$

Divide 36\sqrt{2} by 2\sqrt{3}.

$$x=6\sqrt{6}$$