Solve x=x-z/a

$$x = \frac { x - z } { a }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x-z}{x}\text{, }&x\neq z\text{ and }x\neq 0\\a\neq 0\text{, }&x=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$xa=x-z$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{x-z}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{x-z}{x}$$

Variable a cannot be equal to 0.

$$a=\frac{x-z}{x}\text{, }a\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{z}{a-1}\text{, }&a\neq 1\text{ and }a\neq 0\\x\in \mathrm{R}\text{, }&a=1\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{x-z}{a} from both sides.

$$x-\frac{x-z}{a}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{a}{a}.

$$\frac{xa}{a}-\frac{x-z}{a}=0$$

Since \frac{xa}{a} and \frac{x-z}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xa-\left(x-z\right)}{a}=0$$

Do the multiplications in xa-\left(x-z\right).

$$\frac{xa-x+z}{a}=0$$

Multiply both sides of the equation by a.

$$xa-x+z=0$$

Subtract z from both sides. Anything subtracted from zero gives its negation.

$$xa-x=-z$$

Combine all terms containing x.

$$\left(a-1\right)x=-z$$

Divide both sides by a-1.

$$\frac{\left(a-1\right)x}{a-1}=-\frac{z}{a-1}$$

Dividing by a-1 undoes the multiplication by a-1.

$$x=-\frac{z}{a-1}$$