Solve frac{sqrt{3}}{3}=x/2000+x

$$\frac{ \sqrt{ 3 } }{ 3 } = \frac{ x }{ 2000+x }$$

Solve for x

$$x=1000\left(\sqrt{3}+1\right)\approx 2732.050807569$$

Steps for Solving Linear Equation

Variable x cannot be equal to -2000 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+2000\right), the least common multiple of 3,2000+x.

$$\left(x+2000\right)\sqrt{3}=3x$$

Use the distributive property to multiply x+2000 by \sqrt{3}.

$$x\sqrt{3}+2000\sqrt{3}=3x$$

Subtract 3x from both sides.

$$x\sqrt{3}+2000\sqrt{3}-3x=0$$

Subtract 2000\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$x\sqrt{3}-3x=-2000\sqrt{3}$$

Combine all terms containing x.

$$\left(\sqrt{3}-3\right)x=-2000\sqrt{3}$$

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

$$\frac{\left(\sqrt{3}-3\right)x}{\sqrt{3}-3}=-\frac{2000\sqrt{3}}{\sqrt{3}-3}$$

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

$$x=-\frac{2000\sqrt{3}}{\sqrt{3}-3}$$

Divide -2000\sqrt{3} by \sqrt{3}-3.

$$x=1000\sqrt{3}+1000$$