Solve x_{n}+1=2x_{n}-(x-x_{n})

$$x _ { n } + 1 = 2 x _ { n } - ( x - x _ { n } )$$

Solve for x

$$x=2x_{n}-1$$

Steps for Solving Linear Equation

To find the opposite of x-x_{n}, find the opposite of each term.

$$x_{n}+1=2x_{n}-x+x_{n}$$

Combine 2x_{n} and x_{n} to get 3x_{n}.

$$x_{n}+1=3x_{n}-x$$

Swap sides so that all variable terms are on the left hand side.

$$3x_{n}-x=x_{n}+1$$

Subtract 3x_{n} from both sides.

$$-x=x_{n}+1-3x_{n}$$

Combine x_{n} and -3x_{n} to get -2x_{n}.

$$-x=-2x_{n}+1$$

The equation is in standard form.

$$-x=1-2x_{n}$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{1-2x_{n}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{1-2x_{n}}{-1}$$

Divide -2x_{n}+1 by -1.

$$x=2x_{n}-1$$

Solve for x_n

$$x_{n}=\frac{x+1}{2}$$

Steps for Solving Linear Equation

To find the opposite of x-x_{n}, find the opposite of each term.

$$x_{n}+1=2x_{n}-x+x_{n}$$

Combine 2x_{n} and x_{n} to get 3x_{n}.

$$x_{n}+1=3x_{n}-x$$

Subtract 3x_{n} from both sides.

$$x_{n}+1-3x_{n}=-x$$

Combine x_{n} and -3x_{n} to get -2x_{n}.

$$-2x_{n}+1=-x$$

Subtract 1 from both sides.

$$-2x_{n}=-x-1$$

Divide both sides by -2.

$$\frac{-2x_{n}}{-2}=\frac{-x-1}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x_{n}=\frac{-x-1}{-2}$$

Divide -x-1 by -2.

$$x_{n}=\frac{x+1}{2}$$