Solve varepsilon=mx

$$\varepsilon = m x$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{\epsilon }{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&\epsilon =0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mx=\epsilon$$

The equation is in standard form.

$$xm=\epsilon$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{\epsilon }{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{\epsilon }{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\epsilon }{m}\text{, }&m\neq 0\\x\in \mathrm{C}\text{, }&\epsilon =0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mx=\epsilon$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{\epsilon }{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{\epsilon }{m}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\epsilon }{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&\epsilon =0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mx=\epsilon$$

The equation is in standard form.

$$xm=\epsilon$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{\epsilon }{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{\epsilon }{x}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\epsilon }{m}\text{, }&m\neq 0\\x\in \mathrm{R}\text{, }&\epsilon =0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mx=\epsilon$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{\epsilon }{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{\epsilon }{m}$$