Finite Math Examples

$y - (- 4) = \frac{5}{4} \cdot (x - (- 4))$

Step 1

Rewrite the equation as $\frac{5}{4} \cdot (x - (- 4)) = y - (- 4)$ .

$\frac{5}{4} \cdot (x - (- 4)) = y - (- 4)$

Step 2

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} (\frac{5}{4} \cdot (x - (- 4))) = \frac{4}{5} (y - (- 4))$

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 $\frac{4}{5} (\frac{5}{4} \cdot (x - (- 4)))$ .

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Step 3.1.1.1

Multiply $- 1$ by $- 4$ .

$\frac{4}{5} (\frac{5}{4} \cdot (x + 4)) = \frac{4}{5} (y - (- 4))$

Step 3.1.1.2

Apply the distributive property.

$\frac{4}{5} (\frac{5}{4} x + \frac{5}{4} \cdot 4) = \frac{4}{5} (y - (- 4))$

Step 3.1.1.3

Combine $\frac{5}{4}$ and $x$ .

$\frac{4}{5} (\frac{5 x}{4} + \frac{5}{4} \cdot 4) = \frac{4}{5} (y - (- 4))$

Step 3.1.1.4

Cancel the common factor of $4$ .

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Step 3.1.1.4.1

Cancel the common factor.

$\frac{4}{5} (\frac{5 x}{4} + \frac{5}{4} \cdot 4) = \frac{4}{5} (y - (- 4))$

Step 3.1.1.4.2

Rewrite the expression.

$\frac{4}{5} (\frac{5 x}{4} + 5) = \frac{4}{5} (y - (- 4))$

Step 3.1.1.5

Apply the distributive property.

$\frac{4}{5} \cdot \frac{5 x}{4} + \frac{4}{5} \cdot 5 = \frac{4}{5} (y - (- 4))$

Step 3.1.1.6

Cancel the common factor of $4$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 x}{4} + \frac{4}{5} \cdot 5 = \frac{4}{5} (y - (- 4))$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{5} (5 x) + \frac{4}{5} \cdot 5 = \frac{4}{5} (y - (- 4))$

Step 3.1.1.7

Cancel the common factor of $5$ .

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Step 3.1.1.7.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) + \frac{4}{5} \cdot 5 = \frac{4}{5} (y - (- 4))$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{5} (5 x) + \frac{4}{5} \cdot 5 = \frac{4}{5} (y - (- 4))$

Step 3.1.1.7.3

Rewrite the expression.

$x + \frac{4}{5} \cdot 5 = \frac{4}{5} (y - (- 4))$

Step 3.1.1.8

Cancel the common factor of $5$ .

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Step 3.1.1.8.1

Cancel the common factor.

$x + \frac{4}{5} \cdot 5 = \frac{4}{5} (y - (- 4))$

Step 3.1.1.8.2

Rewrite the expression.

$x + 4 = \frac{4}{5} (y - (- 4))$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{4}{5} (y - (- 4))$ .

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Step 3.2.1.1

Multiply $- 1$ by $- 4$ .

$x + 4 = \frac{4}{5} (y + 4)$

Step 3.2.1.2

Apply the distributive property.

$x + 4 = \frac{4}{5} y + \frac{4}{5} \cdot 4$

Step 3.2.1.3

Combine $\frac{4}{5}$ and $y$ .

$x + 4 = \frac{4 y}{5} + \frac{4}{5} \cdot 4$

Step 3.2.1.4

Multiply $\frac{4}{5} \cdot 4$ .

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Step 3.2.1.4.1

Combine $\frac{4}{5}$ and $4$ .

$x + 4 = \frac{4 y}{5} + \frac{4 \cdot 4}{5}$

Step 3.2.1.4.2

Multiply $4$ by $4$ .

$x + 4 = \frac{4 y}{5} + \frac{16}{5}$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

$x = \frac{4 y}{5} + \frac{16}{5} - 4$

Step 4.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = \frac{4 y}{5} + \frac{16}{5} - 4 \cdot \frac{5}{5}$

Step 4.3

Combine $- 4$ and $\frac{5}{5}$ .

$x = \frac{4 y}{5} + \frac{16}{5} + \frac{- 4 \cdot 5}{5}$

Step 4.4

Combine the numerators over the common denominator.

$x = \frac{4 y}{5} + \frac{16 - 4 \cdot 5}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 4$ by $5$ .

$x = \frac{4 y}{5} + \frac{16 - 20}{5}$

Step 4.5.2

Subtract $20$ from $16$ .

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

Step 4.6

Move the negative in front of the fraction.

$x = \frac{4 y}{5} - \frac{4}{5}$