Solve y=f(x-5)

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

Solve for f (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply f by x-5.

$$y=fx-5f$$

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

$$fx-5f=y$$

Combine all terms containing f.

$$\left(x-5\right)f=y$$

Divide both sides by x-5.

$$\frac{\left(x-5\right)f}{x-5}=\frac{y}{x-5}$$

Dividing by x-5 undoes the multiplication by x-5.

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply f by x-5.

$$y=fx-5f$$

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

$$fx-5f=y$$

Add 5f to both sides.

$$fx=y+5f$$

Divide both sides by f.

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

Dividing by f undoes the multiplication by f.

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

Divide y+5f by f.

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

Solve for f

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

Steps for Solving Linear Equation

Use the distributive property to multiply f by x-5.

$$y=fx-5f$$

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

$$fx-5f=y$$

Combine all terms containing f.

$$\left(x-5\right)f=y$$

Divide both sides by x-5.

$$\frac{\left(x-5\right)f}{x-5}=\frac{y}{x-5}$$

Dividing by x-5 undoes the multiplication by x-5.

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply f by x-5.

$$y=fx-5f$$

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

$$fx-5f=y$$

Add 5f to both sides.

$$fx=y+5f$$

Divide both sides by f.

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

Dividing by f undoes the multiplication by f.

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

Divide y+5f by f.

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