Solve ax-b=c.aneq0

$$a x - b = c . a \neq 0$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Add b to both sides.

$$ax=c+b$$

The equation is in standard form.

$$xa=b+c$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{b+c}{x}$$

Dividing by x undoes the multiplication by x.

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

Solve for a

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

Steps for Solving Linear Equation

Add b to both sides.

$$ax=c+b$$

The equation is in standard form.

$$xa=b+c$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{b+c}{x}$$

Dividing by x undoes the multiplication by x.

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

Solve for b

$$b=ax-c$$

Steps for Solving Linear Equation

Subtract ax from both sides.

$$-b=c-ax$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{c-ax}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{c-ax}{-1}$$

Divide c-ax by -1.

$$b=ax-c$$