Solve y=f(x)-5

$$y = f ( x ) - 5$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{y+5}{x}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&y=-5\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$fx-5=y$$

Add 5 to both sides.

$$fx=y+5$$

The equation is in standard form.

$$xf=y+5$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{y+5}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{y+5}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y+5}{f}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&y=-5\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$fx-5=y$$

Add 5 to both sides.

$$fx=y+5$$

Divide both sides by f.

$$\frac{fx}{f}=\frac{y+5}{f}$$

Dividing by f undoes the multiplication by f.

$$x=\frac{y+5}{f}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{y+5}{x}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&y=-5\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$fx-5=y$$

Add 5 to both sides.

$$fx=y+5$$

The equation is in standard form.

$$xf=y+5$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{y+5}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{y+5}{x}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y+5}{f}\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&y=-5\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$fx-5=y$$

Add 5 to both sides.

$$fx=y+5$$

Divide both sides by f.

$$\frac{fx}{f}=\frac{y+5}{f}$$

Dividing by f undoes the multiplication by f.

$$x=\frac{y+5}{f}$$