Algebra Examples

$S = \frac{r - p}{3}$

Step 1

Rewrite the equation as $\frac{r - p}{3} = S$ .

$\frac{r - p}{3} = S$

Step 2

Multiply both sides by $3$ .

$\frac{r - p}{3} \cdot 3 = S \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{r - p}{3} \cdot 3$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{r - p}{3} \cdot 3 = S \cdot 3$

Step 3.1.1.1.2

Rewrite the expression.

$r - p = S \cdot 3$

Step 3.1.1.2

Reorder $r$ and $- p$ .

$- p + r = S \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Move $3$ to the left of $S$ .

$- p + r = 3 S$

Step 4

Solve for $p$ .

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Step 4.1

Subtract $r$ from both sides of the equation.

$- p = 3 S - r$

Step 4.2

Divide each term in $- p = 3 S - r$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- p = 3 S - r$ by $- 1$ .

$\frac{- p}{- 1} = \frac{3 S}{- 1} + \frac{- r}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{p}{1} = \frac{3 S}{- 1} + \frac{- r}{- 1}$

Step 4.2.2.2

Divide $p$ by $1$ .

$p = \frac{3 S}{- 1} + \frac{- r}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

Move the negative one from the denominator of $\frac{3 S}{- 1}$ .

$p = - 1 \cdot (3 S) + \frac{- r}{- 1}$

Step 4.2.3.1.2

Rewrite $- 1 \cdot (3 S)$ as $- (3 S)$ .

$p = - (3 S) + \frac{- r}{- 1}$

Step 4.2.3.1.3

Multiply $3$ by $- 1$ .

$p = - 3 S + \frac{- r}{- 1}$

Step 4.2.3.1.4

Dividing two negative values results in a positive value.

$p = - 3 S + \frac{r}{1}$

Step 4.2.3.1.5

Divide $r$ by $1$ .

$p = - 3 S + r$