Solve varepsilon-xvarepsilon=9+xg

$$\varepsilon - x \varepsilon = 9 + x g$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=-\frac{x\epsilon -\epsilon +9}{x}\text{, }&x\neq 0\\g\in \mathrm{C}\text{, }&x=0\text{ and }\epsilon =9\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$9+xg=\epsilon -x\epsilon$$

Subtract 9 from both sides.

$$xg=\epsilon -x\epsilon -9$$

The equation is in standard form.

$$xg=-x\epsilon +\epsilon -9$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{-x\epsilon +\epsilon -9}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{-x\epsilon +\epsilon -9}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\epsilon -9}{g+\epsilon }\text{, }&\epsilon \neq -g\\x\in \mathrm{C}\text{, }&\epsilon =9\text{ and }g=-9\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xg from both sides.

$$\epsilon -x\epsilon -xg=9$$

Subtract \epsilon from both sides.

$$-x\epsilon -xg=9-\epsilon$$

Combine all terms containing x.

$$\left(-\epsilon -g\right)x=9-\epsilon$$

The equation is in standard form.

$$\left(-g-\epsilon \right)x=9-\epsilon$$

Divide both sides by -\epsilon -g.

$$\frac{\left(-g-\epsilon \right)x}{-g-\epsilon }=\frac{9-\epsilon }{-g-\epsilon }$$

Dividing by -\epsilon -g undoes the multiplication by -\epsilon -g.

$$x=\frac{9-\epsilon }{-g-\epsilon }$$

Divide -\epsilon +9 by -\epsilon -g.

$$x=-\frac{9-\epsilon }{g+\epsilon }$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{x\epsilon -\epsilon +9}{x}\text{, }&x\neq 0\\g\in \mathrm{R}\text{, }&x=0\text{ and }\epsilon =9\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$9+xg=\epsilon -x\epsilon$$

Subtract 9 from both sides.

$$xg=\epsilon -x\epsilon -9$$

The equation is in standard form.

$$xg=-x\epsilon +\epsilon -9$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{-x\epsilon +\epsilon -9}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{-x\epsilon +\epsilon -9}{x}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\epsilon -9}{g+\epsilon }\text{, }&\epsilon \neq -g\\x\in \mathrm{R}\text{, }&\epsilon =9\text{ and }g=-9\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xg from both sides.

$$\epsilon -x\epsilon -xg=9$$

Subtract \epsilon from both sides.

$$-x\epsilon -xg=9-\epsilon$$

Combine all terms containing x.

$$\left(-\epsilon -g\right)x=9-\epsilon$$

The equation is in standard form.

$$\left(-g-\epsilon \right)x=9-\epsilon$$

Divide both sides by -\epsilon -g.

$$\frac{\left(-g-\epsilon \right)x}{-g-\epsilon }=\frac{9-\epsilon }{-g-\epsilon }$$

Dividing by -\epsilon -g undoes the multiplication by -\epsilon -g.

$$x=\frac{9-\epsilon }{-g-\epsilon }$$

Divide -\epsilon +9 by -\epsilon -g.

$$x=-\frac{9-\epsilon }{g+\epsilon }$$