Solve sqrt{2}+1-sqrt{2}x=x

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$\sqrt{2}+1-\sqrt{2}x-x=0$$

Subtract \sqrt{2} from both sides. Anything subtracted from zero gives its negation.

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

Subtract 1 from both sides.

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

Combine all terms containing x.

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

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

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

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

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

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

$$x=1$$