Solve 2sqrt{2}x+2(x+1)=(2+sqrt{2})x+7

$$2 \sqrt { 2 } x + 2 ( x + 1 ) = ( 2 + \sqrt { 2 } ) x + 7$$

Solve for x

$$x = \frac{5 \sqrt{2}}{2} \approx 3.535533906$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x+1.

$$2\sqrt{2}x+2x+2=\left(2+\sqrt{2}\right)x+7$$

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

$$2\sqrt{2}x+2x+2=2x+\sqrt{2}x+7$$

Subtract 2x from both sides.

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

Combine 2x and -2x to get 0.

$$2\sqrt{2}x+2=\sqrt{2}x+7$$

Subtract \sqrt{2}x from both sides.

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

Combine 2\sqrt{2}x and -\sqrt{2}x to get \sqrt{2}x.

$$\sqrt{2}x+2=7$$

Subtract 2 from both sides.

$$\sqrt{2}x=7-2$$

Subtract 2 from 7 to get 5.

$$\sqrt{2}x=5$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{5}{\sqrt{2}}$$

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

$$x=\frac{5}{\sqrt{2}}$$

Divide 5 by \sqrt{2}.

$$x=\frac{5\sqrt{2}}{2}$$