Solve -1/sqrt{3}x+2=sqrt{3}*x

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

Solve for x

$$x=\frac{\sqrt{3}}{2}\approx 0.866025404$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Express \left(-\frac{\sqrt{3}}{3}\right)x as a single fraction.

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

Subtract \sqrt{3}x from both sides.

$$\frac{-\sqrt{3}x}{3}+2-\sqrt{3}x=0$$

Multiply both sides of the equation by 3.

$$3\left(\frac{-\sqrt{3}x}{3}+2\right)-3\sqrt{3}x=0$$

Multiply both sides of the equation by 3.

$$9\left(\frac{-\sqrt{3}x}{3}+2\right)-3\times 3\sqrt{3}x=0$$

Use the distributive property to multiply 9 by \frac{-\sqrt{3}x}{3}+2.

$$9\times \frac{-\sqrt{3}x}{3}+18-3\times 3\sqrt{3}x=0$$

Cancel out 3, the greatest common factor in 9 and 3.

$$3\left(-1\right)\sqrt{3}x+18-3\times 3\sqrt{3}x=0$$

Multiply 3 and -1 to get -3.

$$-3\sqrt{3}x+18-3\times 3\sqrt{3}x=0$$

Multiply -3 and 3 to get -9.

$$-3\sqrt{3}x+18-9\sqrt{3}x=0$$

Combine -3\sqrt{3}x and -9\sqrt{3}x to get -12\sqrt{3}x.

$$-12\sqrt{3}x+18=0$$

Subtract 18 from both sides. Anything subtracted from zero gives its negation.

$$-12\sqrt{3}x=-18$$

The equation is in standard form.

$$\left(-12\sqrt{3}\right)x=-18$$

Divide both sides by -12\sqrt{3}.

$$\frac{\left(-12\sqrt{3}\right)x}{-12\sqrt{3}}=-\frac{18}{-12\sqrt{3}}$$

Dividing by -12\sqrt{3} undoes the multiplication by -12\sqrt{3}.

$$x=-\frac{18}{-12\sqrt{3}}$$

Divide -18 by -12\sqrt{3}.

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