Solve x=1/4(f(x))+4

$$x = \frac { 1 } { 4 } ( f ( x ) ) + 4$$

Solve for f

$$f=4-\frac{16}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$\frac{1}{4}fx+4=x$$

Subtract 4 from both sides.

$$\frac{1}{4}fx=x-4$$

The equation is in standard form.

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

Divide both sides by \frac{1}{4}x.

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

Dividing by \frac{1}{4}x undoes the multiplication by \frac{1}{4}x.

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

Divide x-4 by \frac{1}{4}x.

$$f=4-\frac{16}{x}$$

Solve for x

$$x=\frac{16}{4-f}$$

$$f\neq 4$$

Steps for Solving Linear Equation

Subtract \frac{1}{4}fx from both sides.

$$x-\frac{1}{4}fx=4$$

Combine all terms containing x.

$$\left(1-\frac{1}{4}f\right)x=4$$

The equation is in standard form.

$$\left(-\frac{f}{4}+1\right)x=4$$

Divide both sides by 1-\frac{1}{4}f.

$$\frac{\left(-\frac{f}{4}+1\right)x}{-\frac{f}{4}+1}=\frac{4}{-\frac{f}{4}+1}$$

Dividing by 1-\frac{1}{4}f undoes the multiplication by 1-\frac{1}{4}f.

$$x=\frac{4}{-\frac{f}{4}+1}$$

Divide 4 by 1-\frac{1}{4}f.

$$x=\frac{16}{4-f}$$