Solve y=f(-x-5)-4

$$y = f ( - x - 5 ) - 4$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{y+4}{x+5}\text{, }&x\neq -5\\f\in \mathrm{C}\text{, }&y=-4\text{ and }x=-5\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=f\left(-x\right)-5f-4$$

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

$$f\left(-x\right)-5f-4=y$$

Add 4 to both sides.

$$f\left(-x\right)-5f=y+4$$

Reorder the terms.

$$-fx-5f=y+4$$

Combine all terms containing f.

$$\left(-x-5\right)f=y+4$$

Divide both sides by -x-5.

$$\frac{\left(-x-5\right)f}{-x-5}=\frac{y+4}{-x-5}$$

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

$$f=\frac{y+4}{-x-5}$$

Divide y+4 by -x-5.

$$f=-\frac{y+4}{x+5}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{y+5f+4}{f}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&y=-4\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=f\left(-x\right)-5f-4$$

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

$$f\left(-x\right)-5f-4=y$$

Add 5f to both sides.

$$f\left(-x\right)-4=y+5f$$

Add 4 to both sides.

$$f\left(-x\right)=y+5f+4$$

Reorder the terms.

$$-fx=y+5f+4$$

The equation is in standard form.

$$\left(-f\right)x=y+5f+4$$

Divide both sides by -f.

$$\frac{\left(-f\right)x}{-f}=\frac{y+5f+4}{-f}$$

Dividing by -f undoes the multiplication by -f.

$$x=\frac{y+5f+4}{-f}$$

Divide y+4+5f by -f.

$$x=-\frac{y+5f+4}{f}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{y+4}{x+5}\text{, }&x\neq -5\\f\in \mathrm{R}\text{, }&y=-4\text{ and }x=-5\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=f\left(-x\right)-5f-4$$

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

$$f\left(-x\right)-5f-4=y$$

Add 4 to both sides.

$$f\left(-x\right)-5f=y+4$$

Reorder the terms.

$$-fx-5f=y+4$$

Combine all terms containing f.

$$\left(-x-5\right)f=y+4$$

Divide both sides by -x-5.

$$\frac{\left(-x-5\right)f}{-x-5}=\frac{y+4}{-x-5}$$

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

$$f=\frac{y+4}{-x-5}$$

Divide y+4 by -x-5.

$$f=-\frac{y+4}{x+5}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y+5f+4}{f}\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&y=-4\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=f\left(-x\right)-5f-4$$

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

$$f\left(-x\right)-5f-4=y$$

Add 5f to both sides.

$$f\left(-x\right)-4=y+5f$$

Add 4 to both sides.

$$f\left(-x\right)=y+5f+4$$

Reorder the terms.

$$-fx=y+5f+4$$

The equation is in standard form.

$$\left(-f\right)x=y+5f+4$$

Divide both sides by -f.

$$\frac{\left(-f\right)x}{-f}=\frac{y+5f+4}{-f}$$

Dividing by -f undoes the multiplication by -f.

$$x=\frac{y+5f+4}{-f}$$

Divide y+4+5f by -f.

$$x=-\frac{y+5f+4}{f}$$