Solve sqrt{2}(x-1)=2(x-2)+3sqrt{2}

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

Solve for x

$$x=-2\sqrt{2}\approx -2.828427125$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{2} by x-1.

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

Use the distributive property to multiply 2 by x-2.

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

Subtract 2x from both sides.

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

Add \sqrt{2} to both sides.

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

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

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

Combine all terms containing x.

$$\left(\sqrt{2}-2\right)x=-4+4\sqrt{2}$$

The equation is in standard form.

$$\left(\sqrt{2}-2\right)x=4\sqrt{2}-4$$

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

$$\frac{\left(\sqrt{2}-2\right)x}{\sqrt{2}-2}=\frac{4\sqrt{2}-4}{\sqrt{2}-2}$$

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

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

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

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