Solve 1-f(x)=2x+2

$$1 - f ( x ) = 2 x + 2$$

Solve for f

$$f=-2-\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$-fx=2x+2-1$$

Subtract 1 from 2 to get 1.

$$-fx=2x+1$$

The equation is in standard form.

$$\left(-x\right)f=2x+1$$

Divide both sides by -x.

$$\frac{\left(-x\right)f}{-x}=\frac{2x+1}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$f=\frac{2x+1}{-x}$$

Divide 2x+1 by -x.

$$f=-2-\frac{1}{x}$$

Solve for x

$$x=\frac{1}{-f-2}$$

$$f\neq -2$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$1-fx-2x=2$$

Subtract 1 from both sides.

$$-fx-2x=2-1$$

Subtract 1 from 2 to get 1.

$$-fx-2x=1$$

Combine all terms containing x.

$$\left(-f-2\right)x=1$$

Divide both sides by -f-2.

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

Dividing by -f-2 undoes the multiplication by -f-2.

$$x=\frac{1}{-f-2}$$