Solve x+7/9-3x+xsqrt{2}=x

$$x+ \frac{ 7 }{ 9 } -3x+x \sqrt{ 2 } = x$$

Solve for x

$$x=\frac{\sqrt{2}+3}{9}\approx 0.490468174$$

Steps for Solving Linear Equation

Combine x and -3x to get -2x.

$$-2x+\frac{7}{9}+x\sqrt{2}=x$$

Subtract x from both sides.

$$-2x+\frac{7}{9}+x\sqrt{2}-x=0$$

Combine -2x and -x to get -3x.

$$-3x+\frac{7}{9}+x\sqrt{2}=0$$

Subtract \frac{7}{9} from both sides. Anything subtracted from zero gives its negation.

$$-3x+x\sqrt{2}=-\frac{7}{9}$$

Combine all terms containing x.

$$\left(-3+\sqrt{2}\right)x=-\frac{7}{9}$$

The equation is in standard form.

$$\left(\sqrt{2}-3\right)x=-\frac{7}{9}$$

Divide both sides by -3+\sqrt{2}.

$$\frac{\left(\sqrt{2}-3\right)x}{\sqrt{2}-3}=-\frac{\frac{7}{9}}{\sqrt{2}-3}$$

Dividing by -3+\sqrt{2} undoes the multiplication by -3+\sqrt{2}.

$$x=-\frac{\frac{7}{9}}{\sqrt{2}-3}$$

Divide -\frac{7}{9} by -3+\sqrt{2}.

$$x=\frac{\sqrt{2}}{9}+\frac{1}{3}$$