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

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

Solve for x

$$x=24$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$2\times 3^{\frac{1}{2}}\times 2=\frac{x}{2\sqrt{3}}$$

Multiply 2 and 2 to get 4.

$$4\times 3^{\frac{1}{2}}=\frac{x}{2\sqrt{3}}$$

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

$$4\times 3^{\frac{1}{2}}=\frac{x\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\times 3^{\frac{1}{2}}=\frac{x\sqrt{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$4\times 3^{\frac{1}{2}}=\frac{x\sqrt{3}}{6}$$

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

$$\frac{x\sqrt{3}}{6}=4\times 3^{\frac{1}{2}}$$

Multiply both sides of the equation by 6.

$$x\sqrt{3}=24\times 3^{\frac{1}{2}}$$

Reorder the terms.

$$\sqrt{3}x=24\sqrt{3}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}x}{\sqrt{3}}=\frac{24\sqrt{3}}{\sqrt{3}}$$

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

$$x=\frac{24\sqrt{3}}{\sqrt{3}}$$

Divide 24\sqrt{3} by \sqrt{3}.

$$x=24$$