Solve f(a)+f(n)=5x-2

$$f ( a ) + f ( n ) = 5 x - 2$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{2+fn-5x}{f}\text{, }&f\neq 0\\a\in \mathrm{C}\text{, }&x=\frac{2}{5}\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract fn from both sides.

$$fa=5x-2-fn$$

The equation is in standard form.

$$fa=5x-fn-2$$

Divide both sides by f.

$$\frac{fa}{f}=\frac{5x-fn-2}{f}$$

Dividing by f undoes the multiplication by f.

$$a=\frac{5x-fn-2}{f}$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{2-5x}{a+n}\text{, }&a\neq -n\\f\in \mathrm{C}\text{, }&x=\frac{2}{5}\text{ and }a=-n\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing f.

$$\left(a+n\right)f=5x-2$$

The equation is in standard form.

$$\left(n+a\right)f=5x-2$$

Divide both sides by a+n.

$$\frac{\left(n+a\right)f}{n+a}=\frac{5x-2}{n+a}$$

Dividing by a+n undoes the multiplication by a+n.

$$f=\frac{5x-2}{n+a}$$

Divide 5x-2 by a+n.

$$f=\frac{5x-2}{a+n}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{2+fn-5x}{f}\text{, }&f\neq 0\\a\in \mathrm{R}\text{, }&x=\frac{2}{5}\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract fn from both sides.

$$fa=5x-2-fn$$

The equation is in standard form.

$$fa=5x-fn-2$$

Divide both sides by f.

$$\frac{fa}{f}=\frac{5x-fn-2}{f}$$

Dividing by f undoes the multiplication by f.

$$a=\frac{5x-fn-2}{f}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{2-5x}{a+n}\text{, }&a\neq -n\\f\in \mathrm{R}\text{, }&x=\frac{2}{5}\text{ and }a=-n\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing f.

$$\left(a+n\right)f=5x-2$$

The equation is in standard form.

$$\left(n+a\right)f=5x-2$$

Divide both sides by a+n.

$$\frac{\left(n+a\right)f}{n+a}=\frac{5x-2}{n+a}$$

Dividing by a+n undoes the multiplication by a+n.

$$f=\frac{5x-2}{n+a}$$

Divide 5x-2 by a+n.

$$f=\frac{5x-2}{a+n}$$