Solve y=f(x+5)

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

Solve for f (complex solution)

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

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.

$$fx+5f=y$$

Subtract 5f from 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

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

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.

$$fx+5f=y$$

Subtract 5f from 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.

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