Solve f(x)=operatorname{Mx}3x

$$f ( x ) = \operatorname { Mx } 3 x$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=\frac{f}{x_{3}}\text{, }&x_{3}\neq 0\\M\in \mathrm{C}\text{, }&x=0\text{ or }\left(f=0\text{ and }x_{3}=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Mx_{3}x=fx$$

The equation is in standard form.

$$xx_{3}M=fx$$

Divide both sides by x_{3}x.

$$\frac{xx_{3}M}{xx_{3}}=\frac{fx}{xx_{3}}$$

Dividing by x_{3}x undoes the multiplication by x_{3}x.

$$M=\frac{fx}{xx_{3}}$$

Divide fx by x_{3}x.

$$M=\frac{f}{x_{3}}$$

Solve for f (complex solution)

$$\left\{\begin{matrix}\\f=Mx_{3}\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=Mxx_{3}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{Mxx_{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{Mxx_{3}}{x}$$

Divide Mx_{3}x by x.

$$f=Mx_{3}$$

Solve for M

$$\left\{\begin{matrix}M=\frac{f}{x_{3}}\text{, }&x_{3}\neq 0\\M\in \mathrm{R}\text{, }&x=0\text{ or }\left(f=0\text{ and }x_{3}=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Mx_{3}x=fx$$

The equation is in standard form.

$$xx_{3}M=fx$$

Divide both sides by x_{3}x.

$$\frac{xx_{3}M}{xx_{3}}=\frac{fx}{xx_{3}}$$

Dividing by x_{3}x undoes the multiplication by x_{3}x.

$$M=\frac{fx}{xx_{3}}$$

Divide fx by x_{3}x.

$$M=\frac{f}{x_{3}}$$

Solve for f

$$\left\{\begin{matrix}\\f=Mx_{3}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=Mxx_{3}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{Mxx_{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{Mxx_{3}}{x}$$

Divide Mx_{3}x by x.

$$f=Mx_{3}$$