Solve x=frac{sqrt{3}}{3}-sqrt{3}x

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

Solve for x

$$x=-\frac{\sqrt{3}}{6}+\frac{1}{2}\approx 0.211324865$$

Steps for Solving Linear Equation

Add \sqrt{3}x to both sides.

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

Multiply both sides of the equation by 3.

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

Combine all terms containing x.

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

The equation is in standard form.

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

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

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

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

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

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

$$x=-\frac{\sqrt{3}}{6}+\frac{1}{2}$$