Solve mx-3=2x+(m-5

$$m x - 3 = 2 x + ( m - 5$$

Solve for m (complex solution)

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

Steps for Solving Linear Equation

Subtract m from both sides.

$$mx-3-m=2x-5$$

Add 3 to both sides.

$$mx-m=2x-5+3$$

Add -5 and 3 to get -2.

$$mx-m=2x-2$$

Combine all terms containing m.

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

Divide both sides by -1+x.

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

Dividing by -1+x undoes the multiplication by -1+x.

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

Divide -2+2x by -1+x.

$$m=2$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$mx-3-2x=m-5$$

Add 3 to both sides.

$$mx-2x=m-5+3$$

Add -5 and 3 to get -2.

$$mx-2x=m-2$$

Combine all terms containing x.

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

Divide both sides by -2+m.

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

Dividing by -2+m undoes the multiplication by -2+m.

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

Divide -2+m by -2+m.

$$x=1$$

Solve for m

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

Steps for Solving Linear Equation

Subtract m from both sides.

$$mx-3-m=2x-5$$

Add 3 to both sides.

$$mx-m=2x-5+3$$

Add -5 and 3 to get -2.

$$mx-m=2x-2$$

Combine all terms containing m.

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

Divide both sides by -1+x.

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

Dividing by -1+x undoes the multiplication by -1+x.

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

Divide -2+2x by -1+x.

$$m=2$$

Solve for x

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

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$mx-3-2x=m-5$$

Add 3 to both sides.

$$mx-2x=m-5+3$$

Add -5 and 3 to get -2.

$$mx-2x=m-2$$

Combine all terms containing x.

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

Divide both sides by -2+m.

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

Dividing by -2+m undoes the multiplication by -2+m.

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

Divide -2+m by -2+m.

$$x=1$$