Finite Math Examples

$y = \frac{900000000 - 30000 x}{x + 90000}$

Step 1

Rewrite the equation as $\frac{900000000 - 30000 x}{x + 90000} = y$ .

$\frac{900000000 - 30000 x}{x + 90000} = y$

Step 2

Factor $30000$ out of $900000000 - 30000 x$ .

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Step 2.1

Factor $30000$ out of $900000000$ .

$\frac{30000 (30000) - 30000 x}{x + 90000} = y$

Step 2.2

Factor $30000$ out of $- 30000 x$ .

$\frac{30000 (30000) + 30000 (- x)}{x + 90000} = y$

Step 2.3

Factor $30000$ out of $30000 (30000) + 30000 (- x)$ .

$\frac{30000 (30000 - x)}{x + 90000} = y$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 90000, 1$

Step 3.2

Remove parentheses.

$x + 90000, 1$

Step 3.3

The LCM of one and any expression is the expression.

$x + 90000$

Step 4

Multiply each term in $\frac{30000 (30000 - x)}{x + 90000} = y$ by $x + 90000$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{30000 (30000 - x)}{x + 90000} = y$ by $x + 90000$ .

$\frac{30000 (30000 - x)}{x + 90000} (x + 90000) = y (x + 90000)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x + 90000$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{30000 (30000 - x)}{x + 90000} (x + 90000) = y (x + 90000)$

Step 4.2.1.2

Rewrite the expression.

$30000 (30000 - x) = y (x + 90000)$

Step 4.2.2

Apply the distributive property.

$30000 \cdot 30000 + 30000 (- x) = y (x + 90000)$

Step 4.2.3

Multiply.

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Step 4.2.3.1

Multiply $30000$ by $30000$ .

$900000000 + 30000 (- x) = y (x + 90000)$

Step 4.2.3.2

Multiply $- 1$ by $30000$ .

$900000000 - 30000 x = y (x + 90000)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Apply the distributive property.

$900000000 - 30000 x = y x + y \cdot 90000$

Step 4.3.2

Move $90000$ to the left of $y$ .

$900000000 - 30000 x = y x + 90000 y$

Step 5

Solve the equation.

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Step 5.1

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

$900000000 - 30000 x - y x = 90000 y$

Step 5.2

Subtract $900000000$ from both sides of the equation.

$- 30000 x - y x = 90000 y - 900000000$

Step 5.3

Factor $x$ out of $- 30000 x - y x$ .

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Step 5.3.1

Factor $x$ out of $- 30000 x$ .

$x \cdot - 30000 - y x = 90000 y - 900000000$

Step 5.3.2

Factor $x$ out of $- y x$ .

$x \cdot - 30000 + x (- y) = 90000 y - 900000000$

Step 5.3.3

Factor $x$ out of $x \cdot - 30000 + x (- y)$ .

$x (- 30000 - y) = 90000 y - 900000000$

Step 5.4

Divide each term in $x (- 30000 - y) = 90000 y - 900000000$ by $- 30000 - y$ and simplify.

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Step 5.4.1

Divide each term in $x (- 30000 - y) = 90000 y - 900000000$ by $- 30000 - y$ .

$\frac{x (- 30000 - y)}{- 30000 - y} = \frac{90000 y}{- 30000 - y} + \frac{- 900000000}{- 30000 - y}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $- 30000 - y$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{x (- 30000 - y)}{- 30000 - y} = \frac{90000 y}{- 30000 - y} + \frac{- 900000000}{- 30000 - y}$

Step 5.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{90000 y}{- 30000 - y} + \frac{- 900000000}{- 30000 - y}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Combine the numerators over the common denominator.

$x = \frac{90000 y - 900000000}{- 30000 - y}$

Step 5.4.3.2

Factor $90000$ out of $90000 y - 900000000$ .

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Step 5.4.3.2.1

Factor $90000$ out of $90000 y$ .

$x = \frac{90000 (y) - 900000000}{- 30000 - y}$

Step 5.4.3.2.2

Factor $90000$ out of $- 900000000$ .

$x = \frac{90000 y + 90000 \cdot - 10000}{- 30000 - y}$

Step 5.4.3.2.3

Factor $90000$ out of $90000 y + 90000 \cdot - 10000$ .

$x = \frac{90000 (y - 10000)}{- 30000 - y}$

Step 5.4.3.3

Rewrite $- 30000$ as $- 1 (30000)$ .

$x = \frac{90000 (y - 10000)}{- 1 (30000) - y}$

Step 5.4.3.4

Factor $- 1$ out of $- y$ .

$x = \frac{90000 (y - 10000)}{- 1 (30000) - (y)}$

Step 5.4.3.5

Factor $- 1$ out of $- 1 (30000) - (y)$ .

$x = \frac{90000 (y - 10000)}{- 1 (30000 + y)}$

Step 5.4.3.6

Move the negative in front of the fraction.

$x = - \frac{90000 (y - 10000)}{30000 + y}$