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

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Subtract \sqrt{2} from both sides.

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

Combine -\sqrt{2} and -\sqrt{2} to get -2\sqrt{2}.

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

Combine all terms containing x.

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

Divide both sides by \sqrt{2}-1.

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

Dividing by \sqrt{2}-1 undoes the multiplication by \sqrt{2}-1.

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

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

$$x=-2$$