Finite Math Examples

$8000000 = 25000 x + 30000 y + 40000 z$ , $280 = x + y + z$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $25000 x + 30000 y + 40000 z = 8000000$ .

$25000 x + 30000 y + 40000 z = 8000000$

$280 = x + y + z$

Step 1.2

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

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Step 1.2.1

Subtract $25000 x$ from both sides of the equation.

$30000 y + 40000 z = 8000000 - 25000 x$

$280 = x + y + z$

Step 1.2.2

Subtract $40000 z$ from both sides of the equation.

$30000 y = 8000000 - 25000 x - 40000 z$

$280 = x + y + z$

$30000 y = 8000000 - 25000 x - 40000 z$

$280 = x + y + z$

Step 1.3

Divide each term in $30000 y = 8000000 - 25000 x - 40000 z$ by $30000$ and simplify.

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Step 1.3.1

Divide each term in $30000 y = 8000000 - 25000 x - 40000 z$ by $30000$ .

$\frac{30000 y}{30000} = \frac{8000000}{30000} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $30000$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{30000 y}{30000} = \frac{8000000}{30000} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8000000}{30000} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

$y = \frac{8000000}{30000} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

$y = \frac{8000000}{30000} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Cancel the common factor of $8000000$ and $30000$ .

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Step 1.3.3.1.1.1

Factor $10000$ out of $8000000$ .

$y = \frac{10000 (800)}{30000} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $10000$ out of $30000$ .

$y = \frac{10000 \cdot 800}{10000 \cdot 3} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{10000 \cdot 800}{10000 \cdot 3} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{800}{3} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

$y = \frac{800}{3} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

$y = \frac{800}{3} + \frac{- 25000 x}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.2

Cancel the common factor of $- 25000$ and $30000$ .

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Step 1.3.3.1.2.1

Factor $5000$ out of $- 25000 x$ .

$y = \frac{800}{3} + \frac{5000 (- 5 x)}{30000} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $5000$ out of $30000$ .

$y = \frac{800}{3} + \frac{5000 (- 5 x)}{5000 (6)} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.2.2.2

Cancel the common factor.

$y = \frac{800}{3} + \frac{5000 (- 5 x)}{5000 \cdot 6} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.2.2.3

Rewrite the expression.

$y = \frac{800}{3} + \frac{- 5 x}{6} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

$y = \frac{800}{3} + \frac{- 5 x}{6} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

$y = \frac{800}{3} + \frac{- 5 x}{6} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.3

Move the negative in front of the fraction.

$y = \frac{800}{3} - \frac{5 x}{6} + \frac{- 40000 z}{30000}$

$280 = x + y + z$

Step 1.3.3.1.4

Cancel the common factor of $- 40000$ and $30000$ .

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Step 1.3.3.1.4.1

Factor $10000$ out of $- 40000 z$ .

$y = \frac{800}{3} - \frac{5 x}{6} + \frac{10000 (- 4 z)}{30000}$

$280 = x + y + z$

Step 1.3.3.1.4.2

Cancel the common factors.

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Step 1.3.3.1.4.2.1

Factor $10000$ out of $30000$ .

$y = \frac{800}{3} - \frac{5 x}{6} + \frac{10000 (- 4 z)}{10000 (3)}$

$280 = x + y + z$

Step 1.3.3.1.4.2.2

Cancel the common factor.

$y = \frac{800}{3} - \frac{5 x}{6} + \frac{10000 (- 4 z)}{10000 \cdot 3}$

$280 = x + y + z$

Step 1.3.3.1.4.2.3

Rewrite the expression.

$y = \frac{800}{3} - \frac{5 x}{6} + \frac{- 4 z}{3}$

$280 = x + y + z$

$y = \frac{800}{3} - \frac{5 x}{6} + \frac{- 4 z}{3}$

$280 = x + y + z$

$y = \frac{800}{3} - \frac{5 x}{6} + \frac{- 4 z}{3}$

$280 = x + y + z$

Step 1.3.3.1.5

Move the negative in front of the fraction.

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$280 = x + y + z$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$280 = x + y + z$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$280 = x + y + z$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$280 = x + y + z$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$280 = x + y + z$

Step 2

Solve the equation for $z$ .

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Step 2.1

Rewrite the equation as $x + \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3} + z = 280$ .

$x + \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3} + z = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2

Simplify $x + \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3} + z$ .

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Step 2.2.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$x \cdot \frac{6}{6} - \frac{5 x}{6} + \frac{800}{3} - \frac{4 z}{3} + z = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.2

Combine $x$ and $\frac{6}{6}$ .

$\frac{x \cdot 6}{6} - \frac{5 x}{6} + \frac{800}{3} - \frac{4 z}{3} + z = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{x \cdot 6 - 5 x}{6} + \frac{800}{3} - \frac{4 z}{3} + z = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.4

Subtract $5 x$ from $x \cdot 6$ .

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Step 2.2.4.1

Reorder $x$ and $6$ .

$\frac{6 \cdot x - 5 x}{6} + \frac{800}{3} - \frac{4 z}{3} + z = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.4.2

Subtract $5 x$ from $6 \cdot x$ .

$\frac{x}{6} + \frac{800}{3} - \frac{4 z}{3} + z = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$\frac{x}{6} + \frac{800}{3} - \frac{4 z}{3} + z = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.5

To write $z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{6} + \frac{800}{3} - \frac{4 z}{3} + z \cdot \frac{3}{3} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.6

Simplify terms.

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Step 2.2.6.1

Combine $z$ and $\frac{3}{3}$ .

$\frac{x}{6} + \frac{800}{3} - \frac{4 z}{3} + \frac{z \cdot 3}{3} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.6.2

Combine the numerators over the common denominator.

$\frac{x}{6} + \frac{800}{3} + \frac{- 4 z + z \cdot 3}{3} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.6.3

Combine the numerators over the common denominator.

$\frac{x}{6} + \frac{800 - 4 z + z \cdot 3}{3} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$\frac{x}{6} + \frac{800 - 4 z + z \cdot 3}{3} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.7

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

$\frac{x}{6} + \frac{800 - 4 z + 3 z}{3} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.8

Add $- 4 z$ and $3 z$ .

$\frac{x}{6} + \frac{800 - z}{3} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.9

To write $\frac{800 - z}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{6} + \frac{800 - z}{3} \cdot \frac{2}{2} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.10

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.10.1

Multiply $\frac{800 - z}{3}$ by $\frac{2}{2}$ .

$\frac{x}{6} + \frac{(800 - z) \cdot 2}{3 \cdot 2} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.10.2

Multiply $3$ by $2$ .

$\frac{x}{6} + \frac{(800 - z) \cdot 2}{6} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$\frac{x}{6} + \frac{(800 - z) \cdot 2}{6} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.11

Combine the numerators over the common denominator.

$\frac{x + (800 - z) \cdot 2}{6} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.12

Simplify the numerator.

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Step 2.2.12.1

Apply the distributive property.

$\frac{x + 800 \cdot 2 - z \cdot 2}{6} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.12.2

Multiply $800$ by $2$ .

$\frac{x + 1600 - z \cdot 2}{6} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.2.12.3

Multiply $2$ by $- 1$ .

$\frac{x + 1600 - 2 z}{6} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$\frac{x + 1600 - 2 z}{6} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$\frac{x + 1600 - 2 z}{6} = 280$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.3

Multiply both sides by $6$ .

$\frac{x + 1600 - 2 z}{6} \cdot 6 = 280 \cdot 6$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.4

Simplify.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Simplify $\frac{x + 1600 - 2 z}{6} \cdot 6$ .

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Step 2.4.1.1.1

Cancel the common factor of $6$ .

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Step 2.4.1.1.1.1

Cancel the common factor.

$\frac{x + 1600 - 2 z}{6} \cdot 6 = 280 \cdot 6$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.4.1.1.1.2

Rewrite the expression.

$x + 1600 - 2 z = 280 \cdot 6$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$x + 1600 - 2 z = 280 \cdot 6$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.4.1.1.2

Move $1600$ .

$x - 2 z + 1600 = 280 \cdot 6$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$x - 2 z + 1600 = 280 \cdot 6$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$x - 2 z + 1600 = 280 \cdot 6$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Multiply $280$ by $6$ .

$x - 2 z + 1600 = 1680$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$x - 2 z + 1600 = 1680$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$x - 2 z + 1600 = 1680$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.5

Solve for $z$ .

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Step 2.5.1

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

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Step 2.5.1.1

Subtract $x$ from both sides of the equation.

$- 2 z + 1600 = 1680 - x$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.5.1.2

Subtract $1600$ from both sides of the equation.

$- 2 z = 1680 - x - 1600$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.5.1.3

Subtract $1600$ from $1680$ .

$- 2 z = - x + 80$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$- 2 z = - x + 80$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.5.2

Divide each term in $- 2 z = - x + 80$ by $- 2$ and simplify.

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Step 2.5.2.1

Divide each term in $- 2 z = - x + 80$ by $- 2$ .

$\frac{- 2 z}{- 2} = \frac{- x}{- 2} + \frac{80}{- 2}$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.5.2.2

Simplify the left side.

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Step 2.5.2.2.1

Cancel the common factor of $- 2$ .

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Step 2.5.2.2.1.1

Cancel the common factor.

$\frac{- 2 z}{- 2} = \frac{- x}{- 2} + \frac{80}{- 2}$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.5.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{- x}{- 2} + \frac{80}{- 2}$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$z = \frac{- x}{- 2} + \frac{80}{- 2}$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$z = \frac{- x}{- 2} + \frac{80}{- 2}$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.5.2.3

Simplify the right side.

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Step 2.5.2.3.1

Simplify each term.

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Step 2.5.2.3.1.1

Dividing two negative values results in a positive value.

$z = \frac{x}{2} + \frac{80}{- 2}$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 2.5.2.3.1.2

Divide $80$ by $- 2$ .

$z = \frac{x}{2} - 40$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$z = \frac{x}{2} - 40$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$z = \frac{x}{2} - 40$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$z = \frac{x}{2} - 40$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$z = \frac{x}{2} - 40$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

$z = \frac{x}{2} - 40$

$y = \frac{800}{3} - \frac{5 x}{6} - \frac{4 z}{3}$

Step 3

Simplify the right side.

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Step 3.1

Simplify $\frac{800}{3} - \frac{5 x}{6} - \frac{4 (\frac{x}{2} - 40)}{3}$ .

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Step 3.1.1

Combine the numerators over the common denominator.

$y = \frac{800 - 4 (\frac{x}{2} - 40)}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.2

Simplify each term.

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Step 3.1.2.1

Apply the distributive property.

$y = \frac{800 - 4 \frac{x}{2} - 4 \cdot - 40}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.2.2

Cancel the common factor of $2$ .

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Step 3.1.2.2.1

Factor $2$ out of $- 4$ .

$y = \frac{800 + 2 (- 2) (\frac{x}{2}) - 4 \cdot - 40}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.2.2.2

Cancel the common factor.

$y = \frac{800 + 2 \cdot (- 2 \frac{x}{2}) - 4 \cdot - 40}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.2.2.3

Rewrite the expression.

$y = \frac{800 - 2 x - 4 \cdot - 40}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

$y = \frac{800 - 2 x - 4 \cdot - 40}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.2.3

Multiply $- 4$ by $- 40$ .

$y = \frac{800 - 2 x + 160}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

$y = \frac{800 - 2 x + 160}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.3

Add $800$ and $160$ .

$y = \frac{- 2 x + 960}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.4

Simplify each term.

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Step 3.1.4.1

Factor $2$ out of $- 2 x + 960$ .

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Step 3.1.4.1.1

Factor $2$ out of $- 2 x$ .

$y = \frac{2 (- x) + 960}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.4.1.2

Factor $2$ out of $960$ .

$y = \frac{2 (- x) + 2 (480)}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.4.1.3

Factor $2$ out of $2 (- x) + 2 (480)$ .

$y = \frac{2 (- x + 480)}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

$y = \frac{2 (- x + 480)}{3} + \frac{- 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.4.2

Move the negative in front of the fraction.

$y = \frac{2 (- x + 480)}{3} - \frac{5 x}{6}$

$z = \frac{x}{2} - 40$

$y = \frac{2 (- x + 480)}{3} - \frac{5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.5

To write $\frac{2 (- x + 480)}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{2 (- x + 480)}{3} \cdot \frac{2}{2} - \frac{5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.6

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1.6.1

Multiply $\frac{2 (- x + 480)}{3}$ by $\frac{2}{2}$ .

$y = \frac{2 (- x + 480) \cdot 2}{3 \cdot 2} - \frac{5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.6.2

Multiply $3$ by $2$ .

$y = \frac{2 (- x + 480) \cdot 2}{6} - \frac{5 x}{6}$

$z = \frac{x}{2} - 40$

$y = \frac{2 (- x + 480) \cdot 2}{6} - \frac{5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.7

Combine the numerators over the common denominator.

$y = \frac{2 (- x + 480) \cdot 2 - 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8

Simplify the numerator.

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Step 3.1.8.1

Apply the distributive property.

$y = \frac{(2 (- x) + 2 \cdot 480) \cdot 2 - 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.2

Multiply $- 1$ by $2$ .

$y = \frac{(- 2 x + 2 \cdot 480) \cdot 2 - 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.3

Multiply $2$ by $480$ .

$y = \frac{(- 2 x + 960) \cdot 2 - 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.4

Apply the distributive property.

$y = \frac{- 2 x \cdot 2 + 960 \cdot 2 - 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.5

Multiply $2$ by $- 2$ .

$y = \frac{- 4 x + 960 \cdot 2 - 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.6

Multiply $960$ by $2$ .

$y = \frac{- 4 x + 1920 - 5 x}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.7

Subtract $5 x$ from $- 4 x$ .

$y = \frac{- 9 x + 1920}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.8

Factor $3$ out of $- 9 x + 1920$ .

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Step 3.1.8.8.1

Factor $3$ out of $- 9 x$ .

$y = \frac{3 (- 3 x) + 1920}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.8.2

Factor $3$ out of $1920$ .

$y = \frac{3 (- 3 x) + 3 (640)}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.8.8.3

Factor $3$ out of $3 (- 3 x) + 3 (640)$ .

$y = \frac{3 (- 3 x + 640)}{6}$

$z = \frac{x}{2} - 40$

$y = \frac{3 (- 3 x + 640)}{6}$

$z = \frac{x}{2} - 40$

$y = \frac{3 (- 3 x + 640)}{6}$

$z = \frac{x}{2} - 40$

Step 3.1.9

Cancel the common factors.

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Step 3.1.9.1

Factor $3$ out of $6$ .

$y = \frac{3 (- 3 x + 640)}{3 \cdot 2}$

$z = \frac{x}{2} - 40$

Step 3.1.9.2

Cancel the common factor.

$y = \frac{3 (- 3 x + 640)}{3 \cdot 2}$

$z = \frac{x}{2} - 40$

Step 3.1.9.3

Rewrite the expression.

$y = \frac{- 3 x + 640}{2}$

$z = \frac{x}{2} - 40$

$y = \frac{- 3 x + 640}{2}$

$z = \frac{x}{2} - 40$

Step 3.1.10

Factor $- 1$ out of $- 3 x$ .

$y = \frac{- (3 x) + 640}{2}$

$z = \frac{x}{2} - 40$

Step 3.1.11

Rewrite $640$ as $- 1 (- 640)$ .

$y = \frac{- (3 x) - 1 \cdot - 640}{2}$

$z = \frac{x}{2} - 40$

Step 3.1.12

Factor $- 1$ out of $- (3 x) - 1 (- 640)$ .

$y = \frac{- (3 x - 640)}{2}$

$z = \frac{x}{2} - 40$

Step 3.1.13

Simplify the expression.

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Step 3.1.13.1

Rewrite $- (3 x - 640)$ as $- 1 (3 x - 640)$ .

$y = \frac{- 1 (3 x - 640)}{2}$

$z = \frac{x}{2} - 40$

Step 3.1.13.2

Move the negative in front of the fraction.

$y = - \frac{3 x - 640}{2}$

$z = \frac{x}{2} - 40$

$y = - \frac{3 x - 640}{2}$

$z = \frac{x}{2} - 40$

$y = - \frac{3 x - 640}{2}$

$z = \frac{x}{2} - 40$

$y = - \frac{3 x - 640}{2}$

$z = \frac{x}{2} - 40$