Solve x-b=ax+c

$$x - b = a x + c$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$ax+c=x-b$$

Subtract c from both sides.

$$ax=x-b-c$$

The equation is in standard form.

$$xa=x-b-c$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Solve for a

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

Steps for Solving Linear Equation

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

$$ax+c=x-b$$

Subtract c from both sides.

$$ax=x-b-c$$

The equation is in standard form.

$$xa=x-b-c$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Solve for b

$$b=-ax+x-c$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$-b=ax+c-x$$

The equation is in standard form.

$$-b=ax-x+c$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -x+ax+c by -1.

$$b=-ax+x-c$$