Solve frac{4sqrt{3}}{x}=frac{sqrt{2}}{2}

$$\frac{ 4 \sqrt{ 3 } }{ x } = \frac{ \sqrt{ 2 } }{ 2 }$$

Solve for x

$$x=4\sqrt{6}\approx 9.797958971$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2.

$$2\times 4\sqrt{3}=x\sqrt{2}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{3}=x\sqrt{2}$$

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

$$x\sqrt{2}=8\sqrt{3}$$

The equation is in standard form.

$$\sqrt{2}x=8\sqrt{3}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{8\sqrt{3}}{\sqrt{2}}$$

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

$$x=\frac{8\sqrt{3}}{\sqrt{2}}$$

Divide 8\sqrt{3} by \sqrt{2}.

$$x=4\sqrt{6}$$