Solve 2x+sqrt{6}-sqrt{2}x=2-sqrt{6}x+sqrt{2}

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

Solve for x

$$x=\sqrt{3}-\sqrt{2}\approx 0.317837245$$

Steps for Solving Linear Equation

Subtract 2-\sqrt{6}x from both sides.

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

To find the opposite of 2-\sqrt{6}x, find the opposite of each term.

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

The opposite of -\sqrt{6}x is \sqrt{6}x.

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

Subtract \sqrt{6} from both sides.

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

Add 2 to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2-\sqrt{2}+\sqrt{6}.

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

Dividing by 2-\sqrt{2}+\sqrt{6} undoes the multiplication by 2-\sqrt{2}+\sqrt{6}.

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

Divide \sqrt{2}-\sqrt{6}+2 by 2-\sqrt{2}+\sqrt{6}.

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