Finite Math Examples

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

Step 1

Rewrite the equation as $- \frac{2}{5} \cdot (x - 5) = y + 1$ .

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

Step 2

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

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

Simplify terms.

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Step 3.1.1.1.1

Apply the distributive property.

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

Step 3.1.1.1.2

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

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

Step 3.1.1.1.3

Cancel the common factor of $5$ .

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Step 3.1.1.1.3.1

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

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

Step 3.1.1.1.3.2

Factor $5$ out of $- 5$ .

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

Step 3.1.1.1.3.3

Cancel the common factor.

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

Step 3.1.1.1.3.4

Rewrite the expression.

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

Step 3.1.1.1.4

Multiply $- 2$ by $- 1$ .

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

Step 3.1.1.2

Move $2$ to the left of $x$ .

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

Step 3.1.1.3

Simplify terms.

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Step 3.1.1.3.1

Apply the distributive property.

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

Step 3.1.1.3.2

Cancel the common factor of $5$ .

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Step 3.1.1.3.2.1

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

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

Step 3.1.1.3.2.2

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

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

Step 3.1.1.3.2.3

Factor $5$ out of $- 5$ .

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

Step 3.1.1.3.2.4

Cancel the common factor.

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

Step 3.1.1.3.2.5

Rewrite the expression.

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

Step 3.1.1.3.3

Cancel the common factor of $2$ .

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Step 3.1.1.3.3.1

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

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

Step 3.1.1.3.3.2

Cancel the common factor.

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

Step 3.1.1.3.3.3

Rewrite the expression.

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

Step 3.1.1.3.4

Multiply.

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Step 3.1.1.3.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.1.3.4.2

Multiply $x$ by $1$ .

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

Step 3.1.1.3.5

Cancel the common factor of $2$ .

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Step 3.1.1.3.5.1

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

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

Step 3.1.1.3.5.2

Cancel the common factor.

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

Step 3.1.1.3.5.3

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{5}{2} (y + 1)$ .

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Step 3.2.1.1

Simplify terms.

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Step 3.2.1.1.1

Apply the distributive property.

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

Step 3.2.1.1.2

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

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

Step 3.2.1.1.3

Multiply $- 1$ by $1$ .

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

Step 3.2.1.2

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

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

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

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

Step 4.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $5$ by $2$ .

$x = - \frac{5 y}{2} + \frac{- 5 + 10}{2}$

Step 4.5.2

Add $- 5$ and $10$ .

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