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

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

Solve for x

$$x=6\left(\sqrt{2}-1\right)\approx 2.485281374$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{2x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

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

Subtract x\sqrt{2} from both sides.

$$6-x-x\sqrt{2}=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

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

Combine all terms containing x.

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

The equation is in standard form.

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

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

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

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

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

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

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