Basic Math Examples

$y = 0.8 y + 700 - 5000 r$

Step 1

Rewrite the equation as $0.8 y + 700 - 5000 r = y$ .

$0.8 y + 700 - 5000 r = y$

Step 2

Move all terms not containing $r$ to the right side of the equation.

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Step 2.1

Subtract $0.8 y$ from both sides of the equation.

$700 - 5000 r = y - 0.8 y$

Step 2.2

Subtract $700$ from both sides of the equation.

$- 5000 r = y - 0.8 y - 700$

Step 2.3

Subtract $0.8 y$ from $y$ .

$- 5000 r = 0.2 y - 700$

Step 3

Divide each term in $- 5000 r = 0.2 y - 700$ by $- 5000$ and simplify.

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Step 3.1

Divide each term in $- 5000 r = 0.2 y - 700$ by $- 5000$ .

$\frac{- 5000 r}{- 5000} = \frac{0.2 y}{- 5000} + \frac{- 700}{- 5000}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5000$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 5000 r}{- 5000} = \frac{0.2 y}{- 5000} + \frac{- 700}{- 5000}$

Step 3.2.1.2

Divide $r$ by $1$ .

$r = \frac{0.2 y}{- 5000} + \frac{- 700}{- 5000}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative in front of the fraction.

$r = - \frac{0.2 y}{5000} + \frac{- 700}{- 5000}$

Step 3.3.1.2

Factor $0.2$ out of $0.2 y$ .

$r = - \frac{0.2 (y)}{5000} + \frac{- 700}{- 5000}$

Step 3.3.1.3

Factor $5000$ out of $5000$ .

$r = - \frac{0.2 (y)}{5000 (1)} + \frac{- 700}{- 5000}$

Step 3.3.1.4

Separate fractions.

$r = - (\frac{0.2}{5000} \cdot \frac{y}{1}) + \frac{- 700}{- 5000}$

Step 3.3.1.5

Divide $0.2$ by $5000$ .

$r = - (0.00004 \frac{y}{1}) + \frac{- 700}{- 5000}$

Step 3.3.1.6

Cancel the common factor of $0.00004$ .

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Step 3.3.1.6.1

Factor $0.00004$ out of $1$ .

$r = - (0.00004 \frac{y}{0.00004 \cdot 25000}) + \frac{- 700}{- 5000}$

Step 3.3.1.6.2

Cancel the common factor.

$r = - (0.00004 \frac{y}{0.00004 \cdot 25000}) + \frac{- 700}{- 5000}$

Step 3.3.1.6.3

Rewrite the expression.

$r = - \frac{y}{25000} + \frac{- 700}{- 5000}$

Step 3.3.1.7

Cancel the common factor of $- 700$ and $- 5000$ .

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Step 3.3.1.7.1

Factor $- 100$ out of $- 700$ .

$r = - \frac{y}{25000} + \frac{- 100 (7)}{- 5000}$

Step 3.3.1.7.2

Cancel the common factors.

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Step 3.3.1.7.2.1

Factor $- 100$ out of $- 5000$ .

$r = - \frac{y}{25000} + \frac{- 100 \cdot 7}{- 100 \cdot 50}$

Step 3.3.1.7.2.2

Cancel the common factor.

$r = - \frac{y}{25000} + \frac{- 100 \cdot 7}{- 100 \cdot 50}$

Step 3.3.1.7.2.3

Rewrite the expression.

$r = - \frac{y}{25000} + \frac{7}{50}$