Solve for y v=(x-y)/z

$v = \frac{x - y}{z}$

Step 1

Rewrite the equation as $\frac{x - y}{z} = v$ .

$\frac{x - y}{z} = v$

Step 2

Multiply both sides by $z$ .

$\frac{x - y}{z} z = v z$

Step 3

Simplify the left side.

Cancel the common factor of $z$ .

Cancel the common factor.

$\frac{x - y}{z} z = v z$

Rewrite the expression.

$x - y = v z$

Step 4

Solve for $y$ .

Subtract $x$ from both sides of the equation.

$- y = v z - x$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

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

Rewrite $- 1 \cdot (v z)$ as $- (v z)$ .

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

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

$y = - v z + x$