Solve ax=bx+u

$$a x = b x + u$$

Solve for a

$$\left\{\begin{matrix}a=b+\frac{u}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&u=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xa=bx+u$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{bx+u}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{bx+u}{x}$$

Divide u+bx by x.

$$a=b+\frac{u}{x}$$

Solve for b

$$\left\{\begin{matrix}b=a-\frac{u}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&u=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$bx+u=ax$$

Subtract u from both sides.

$$bx=ax-u$$

The equation is in standard form.

$$xb=ax-u$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{ax-u}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{ax-u}{x}$$

Divide ax-u by x.

$$b=a-\frac{u}{x}$$