Solve 8/3sqrt{3}+x/sqrt{3}=x

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

Solve for x

$$x=4\left(\sqrt{3}+1\right)\approx 10.92820323$$

Steps for Solving Linear Equation

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

$$\frac{8}{3}\sqrt{3}+\frac{x\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=x$$

The square of \sqrt{3} is 3.

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

Subtract x from both sides.

$$\frac{8}{3}\sqrt{3}+\frac{x\sqrt{3}}{3}-x=0$$

Subtract \frac{8}{3}\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

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

Multiply both sides of the equation by 3.

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

Combine all terms containing x.

$$\left(\sqrt{3}-3\right)x=-8\sqrt{3}$$

Divide both sides by \sqrt{3}-3.

$$\frac{\left(\sqrt{3}-3\right)x}{\sqrt{3}-3}=-\frac{8\sqrt{3}}{\sqrt{3}-3}$$

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

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

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

$$x=4\sqrt{3}+4$$