Solve 2x+sqrt{2}=3x-4-3sqrt{2}

$$2 x + \sqrt { 2 } = 3 x - 4 - 3 \sqrt { 2 }$$

Solve for x

$$x=4\left(\sqrt{2}+1\right)\approx 9.656854249$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

$$2x+\sqrt{2}-3x=-4-3\sqrt{2}$$

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

$$-x+\sqrt{2}=-4-3\sqrt{2}$$

Subtract \sqrt{2} from both sides.

$$-x=-4-3\sqrt{2}-\sqrt{2}$$

Combine -3\sqrt{2} and -\sqrt{2} to get -4\sqrt{2}.

$$-x=-4-4\sqrt{2}$$

The equation is in standard form.

$$-x=-4\sqrt{2}-4$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{-4\sqrt{2}-4}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{-4\sqrt{2}-4}{-1}$$

Divide -4-4\sqrt{2} by -1.

$$x=4\sqrt{2}+4$$