Solve x-2=kx-2k

$$x - 2 = k x - 2 k$$

Solve for k (complex solution)

$$\left\{\begin{matrix}\\k=1\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$kx-2k=x-2$$

Combine all terms containing k.

$$\left(x-2\right)k=x-2$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)k}{x-2}=\frac{x-2}{x-2}$$

Dividing by x-2 undoes the multiplication by x-2.

$$k=\frac{x-2}{x-2}$$

Divide x-2 by x-2.

$$k=1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&k=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract kx from both sides.

$$x-2-kx=-2k$$

Add 2 to both sides.

$$x-kx=-2k+2$$

Combine all terms containing x.

$$\left(1-k\right)x=-2k+2$$

The equation is in standard form.

$$\left(1-k\right)x=2-2k$$

Divide both sides by 1-k.

$$\frac{\left(1-k\right)x}{1-k}=\frac{2-2k}{1-k}$$

Dividing by 1-k undoes the multiplication by 1-k.

$$x=\frac{2-2k}{1-k}$$

Divide -2k+2 by 1-k.

$$x=2$$

Solve for k

$$\left\{\begin{matrix}\\k=1\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$kx-2k=x-2$$

Combine all terms containing k.

$$\left(x-2\right)k=x-2$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)k}{x-2}=\frac{x-2}{x-2}$$

Dividing by x-2 undoes the multiplication by x-2.

$$k=\frac{x-2}{x-2}$$

Divide x-2 by x-2.

$$k=1$$

Solve for x

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&k=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract kx from both sides.

$$x-2-kx=-2k$$

Add 2 to both sides.

$$x-kx=-2k+2$$

Combine all terms containing x.

$$\left(1-k\right)x=-2k+2$$

The equation is in standard form.

$$\left(1-k\right)x=2-2k$$

Divide both sides by 1-k.

$$\frac{\left(1-k\right)x}{1-k}=\frac{2-2k}{1-k}$$

Dividing by 1-k undoes the multiplication by 1-k.

$$x=\frac{2-2k}{1-k}$$

Divide -2k+2 by 1-k.

$$x=2$$