Solve 3x-1=2xsqrt{2}-2

$$3 x - 1 = 2 x \sqrt { 2 } - 2$$

Solve for x

$$x=-2\sqrt{2}-3\approx -5.828427125$$

Steps for Solving Linear Equation

Subtract 2x\sqrt{2} from both sides.

$$3x-1-2x\sqrt{2}=-2$$

Add 1 to both sides.

$$3x-2x\sqrt{2}=-2+1$$

Add -2 and 1 to get -1.

$$3x-2x\sqrt{2}=-1$$

Combine all terms containing x.

$$\left(3-2\sqrt{2}\right)x=-1$$

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

$$\frac{\left(3-2\sqrt{2}\right)x}{3-2\sqrt{2}}=-\frac{1}{3-2\sqrt{2}}$$

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

$$x=-\frac{1}{3-2\sqrt{2}}$$

Divide -1 by 3-2\sqrt{2}.

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