Solve A+XA=A+4B

$$A + X A = A + 4 B$$

Solve for A

$$\left\{\begin{matrix}A=\frac{4B}{X}\text{, }&X\neq 0\\A\in \mathrm{R}\text{, }&B=0\text{ and }X=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract A from both sides.

$$A+XA-A=4B$$

Combine A and -A to get 0.

$$XA=4B$$

Divide both sides by X.

$$\frac{XA}{X}=\frac{4B}{X}$$

Dividing by X undoes the multiplication by X.

$$A=\frac{4B}{X}$$

Solve for B

$$B=\frac{AX}{4}$$

Steps for Solving Linear Equation

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

$$A+4B=A+XA$$

Subtract A from both sides.

$$4B=A+XA-A$$

Combine A and -A to get 0.

$$4B=XA$$

The equation is in standard form.

$$4B=AX$$

Divide both sides by 4.

$$\frac{4B}{4}=\frac{AX}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$B=\frac{AX}{4}$$