Solve x=ax+a-b

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{x+b}{x+1}\text{, }&x\neq -1\\a\in \mathrm{C}\text{, }&x=-1\text{ and }b=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax+a-b=x$$

Add b to both sides.

$$ax+a=x+b$$

Combine all terms containing a.

$$\left(x+1\right)a=x+b$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)a}{x+1}=\frac{x+b}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$a=\frac{x+b}{x+1}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x+b}{x+1}\text{, }&x\neq -1\\a\in \mathrm{R}\text{, }&x=-1\text{ and }b=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax+a-b=x$$

Add b to both sides.

$$ax+a=x+b$$

Combine all terms containing a.

$$\left(x+1\right)a=x+b$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)a}{x+1}=\frac{x+b}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$a=\frac{x+b}{x+1}$$

Solve for b

$$b=ax-x+a$$

Steps for Solving Linear Equation

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

$$ax+a-b=x$$

Subtract ax from both sides.

$$a-b=x-ax$$

Subtract a from both sides.

$$-b=x-ax-a$$

The equation is in standard form.

$$-b=-ax+x-a$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide x-ax-a by -1.

$$b=ax-x+a$$