Solve frac{2-2sqrt{2}y}{2}+sqrt{2}y+y=sqrt{2}+3

$$\frac { 2 - 2 \sqrt { 2 } y } { 2 } + \sqrt { 2 } y + y = \sqrt { 2 } + 3$$

Solve for y

$$y=\sqrt{2}+2\approx 3.414213562$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2-2\sqrt{2}y+2\sqrt{2}y+2y=2\sqrt{2}+6$$

Combine -2\sqrt{2}y and 2\sqrt{2}y to get 0.

$$2+2y=2\sqrt{2}+6$$

Subtract 2 from both sides.

$$2y=2\sqrt{2}+6-2$$

Subtract 2 from 6 to get 4.

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

Divide both sides by 2.

$$\frac{2y}{2}=\frac{2\sqrt{2}+4}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{2\sqrt{2}+4}{2}$$

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

$$y=\sqrt{2}+2$$