Solve for z x=y-z

$x = y - z$

Rewrite the equation as $y - z = x$ .

$y - z = x$

Subtract $y$ from both sides of the equation.

$- z = x - y$

Divide each term in $- z = x - y$ by $- 1$ and simplify.

Divide each term in $- z = x - y$ by $- 1$ .

$\frac{- z}{- 1} = \frac{x}{- 1} + \frac{- y}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{x}{- 1} + \frac{- y}{- 1}$

Divide $z$ by $1$ .

$z = \frac{x}{- 1} + \frac{- y}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$z = - 1 \cdot x + \frac{- y}{- 1}$

Rewrite $- 1 \cdot x$ as $- x$ .

$z = - x + \frac{- y}{- 1}$

Dividing two negative values results in a positive value.

$z = - x + \frac{y}{1}$

Divide $y$ by $1$ .

$z = - x + y$