Solve AX=x-B

$$A X = x - B$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-\frac{B-x}{X}\text{, }&X\neq 0\\A\in \mathrm{C}\text{, }&x=B\text{ and }X=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$XA=x-B$$

Divide both sides by X.

$$\frac{XA}{X}=\frac{x-B}{X}$$

Dividing by X undoes the multiplication by X.

$$A=\frac{x-B}{X}$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{B-x}{X}\text{, }&X\neq 0\\A\in \mathrm{R}\text{, }&x=B\text{ and }X=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$XA=x-B$$

Divide both sides by X.

$$\frac{XA}{X}=\frac{x-B}{X}$$

Dividing by X undoes the multiplication by X.

$$A=\frac{x-B}{X}$$

Solve for B

$$B=x-AX$$

Steps for Solving Linear Equation

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

$$x-B=AX$$

Subtract x from both sides.

$$-B=AX-x$$

Divide both sides by -1.

$$\frac{-B}{-1}=\frac{AX-x}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$B=\frac{AX-x}{-1}$$

Divide AX-x by -1.

$$B=x-AX$$