Finite Math Examples

$y = \frac{- 2 x}{5} + \frac{36}{5}$

Step 1

Rewrite the equation as $\frac{- 2 x}{5} + \frac{36}{5} = y$ .

$\frac{- 2 x}{5} + \frac{36}{5} = y$

Step 2

Move the negative in front of the fraction.

$- \frac{2 x}{5} + \frac{36}{5} = y$

Step 3

Subtract $\frac{36}{5}$ from both sides of the equation.

$- \frac{2 x}{5} = y - \frac{36}{5}$

Step 4

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2 x}{5}) = - \frac{5}{2} (y - \frac{36}{5})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{5}{2} (- \frac{2 x}{5})$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 x}{5}) = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.1.2

Move the leading negative in $- \frac{2 x}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

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

$\frac{- 1}{2} (2 (- x)) = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{5}{2} (y - \frac{36}{5})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{5}{2} (y - \frac{36}{5})$ .

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Step 5.2.1.1

Simplify terms.

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Step 5.2.1.1.1

Apply the distributive property.

$x = - \frac{5}{2} y - \frac{5}{2} (- \frac{36}{5})$

Step 5.2.1.1.2

Combine $y$ and $\frac{5}{2}$ .

$x = - \frac{y \cdot 5}{2} - \frac{5}{2} (- \frac{36}{5})$

Step 5.2.1.1.3

Cancel the common factor of $5$ .

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Step 5.2.1.1.3.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$x = - \frac{y \cdot 5}{2} + \frac{- 5}{2} (- \frac{36}{5})$

Step 5.2.1.1.3.2

Move the leading negative in $- \frac{36}{5}$ into the numerator.

$x = - \frac{y \cdot 5}{2} + \frac{- 5}{2} \cdot \frac{- 36}{5}$

Step 5.2.1.1.3.3

Factor $5$ out of $- 5$ .

$x = - \frac{y \cdot 5}{2} + \frac{5 (- 1)}{2} \cdot \frac{- 36}{5}$

Step 5.2.1.1.3.4

Cancel the common factor.

$x = - \frac{y \cdot 5}{2} + \frac{5 \cdot - 1}{2} \cdot \frac{- 36}{5}$

Step 5.2.1.1.3.5

Rewrite the expression.

$x = - \frac{y \cdot 5}{2} + \frac{- 1}{2} \cdot - 36$

Step 5.2.1.1.4

Cancel the common factor of $2$ .

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Step 5.2.1.1.4.1

Factor $2$ out of $- 36$ .

$x = - \frac{y \cdot 5}{2} + \frac{- 1}{2} \cdot (2 (- 18))$

Step 5.2.1.1.4.2

Cancel the common factor.

$x = - \frac{y \cdot 5}{2} + \frac{- 1}{2} \cdot (2 \cdot - 18)$

Step 5.2.1.1.4.3

Rewrite the expression.

$x = - \frac{y \cdot 5}{2} - - 18$

Step 5.2.1.1.5

Multiply $- 1$ by $- 18$ .

$x = - \frac{y \cdot 5}{2} + 18$

Step 5.2.1.2

Move $5$ to the left of $y$ .

$x = - \frac{5 y}{2} + 18$