Solve (3)2sqrt{3}+x=sqrt{3}x-2

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

Solve for x

$$x=4\sqrt{3}+10\approx 16.92820323$$

Steps for Solving Linear Equation

Multiply 2 and 3 to get 6.

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

Subtract \sqrt{3}x from both sides.

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

Subtract 6\sqrt{3} from both sides.

$$x-\sqrt{3}x=-2-6\sqrt{3}$$

Combine all terms containing x.

$$\left(1-\sqrt{3}\right)x=-2-6\sqrt{3}$$

The equation is in standard form.

$$\left(1-\sqrt{3}\right)x=-6\sqrt{3}-2$$

Divide both sides by 1-\sqrt{3}.

$$\frac{\left(1-\sqrt{3}\right)x}{1-\sqrt{3}}=\frac{-6\sqrt{3}-2}{1-\sqrt{3}}$$

Dividing by 1-\sqrt{3} undoes the multiplication by 1-\sqrt{3}.

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

Divide -2-6\sqrt{3} by 1-\sqrt{3}.

$$x=4\sqrt{3}+10$$