Solve for p S=(r-p)/9

$S = \frac{r - p}{9}$

Step 1

Rewrite the equation as $\frac{r - p}{9} = S$ .

$\frac{r - p}{9} = S$

Step 2

Multiply both sides by $9$ .

$\frac{r - p}{9} \cdot 9 = S \cdot 9$

Step 3

Simplify.

Simplify the left side.

Simplify $\frac{r - p}{9} \cdot 9$ .

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{r - p}{9} \cdot 9 = S \cdot 9$

Rewrite the expression.

$r - p = S \cdot 9$

Reorder $r$ and $- p$ .

$- p + r = S \cdot 9$

Simplify the right side.

Move $9$ to the left of $S$ .

$- p + r = 9 S$

Step 4

Solve for $p$ .

Subtract $r$ from both sides of the equation.

$- p = 9 S - r$

Divide each term in $- p = 9 S - r$ by $- 1$ and simplify.

Divide each term in $- p = 9 S - r$ by $- 1$ .

$\frac{- p}{- 1} = \frac{9 S}{- 1} + \frac{- r}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{p}{1} = \frac{9 S}{- 1} + \frac{- r}{- 1}$

Divide $p$ by $1$ .

$p = \frac{9 S}{- 1} + \frac{- r}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{9 S}{- 1}$ .

$p = - 1 \cdot (9 S) + \frac{- r}{- 1}$

Rewrite $- 1 \cdot (9 S)$ as $- (9 S)$ .

$p = - (9 S) + \frac{- r}{- 1}$

Multiply $9$ by $- 1$ .

$p = - 9 S + \frac{- r}{- 1}$

Dividing two negative values results in a positive value.

$p = - 9 S + \frac{r}{1}$

Divide $r$ by $1$ .

$p = - 9 S + r$