Solve f(x)+f(3x)=8x+4

$$f ( x ) + f ( 3 x ) = 8 x + 4$$

Solve for f

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

$$x\neq 0$$

Steps for Solving Linear Equation

Combine fx and f\times 3x to get 4fx.

$$4fx=8x+4$$

The equation is in standard form.

$$4xf=8x+4$$

Divide both sides by 4x.

$$\frac{4xf}{4x}=\frac{8x+4}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$f=\frac{8x+4}{4x}$$

Divide 8x+4 by 4x.

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

Solve for x

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

$$f\neq 2$$

Steps for Solving Linear Equation

Combine fx and f\times 3x to get 4fx.

$$4fx=8x+4$$

Subtract 8x from both sides.

$$4fx-8x=4$$

Combine all terms containing x.

$$\left(4f-8\right)x=4$$

Divide both sides by 4f-8.

$$\frac{\left(4f-8\right)x}{4f-8}=\frac{4}{4f-8}$$

Dividing by 4f-8 undoes the multiplication by 4f-8.

$$x=\frac{4}{4f-8}$$

Divide 4 by 4f-8.

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