Finite Math Examples

$y - 8 = \frac{7}{5} \cdot (x + 10)$

Step 1

Rewrite the equation as $\frac{7}{5} \cdot (x + 10) = y - 8$ .

$\frac{7}{5} \cdot (x + 10) = y - 8$

Step 2

Multiply both sides of the equation by $\frac{5}{7}$ .

$\frac{5}{7} (\frac{7}{5} \cdot (x + 10)) = \frac{5}{7} (y - 8)$

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 $\frac{5}{7} (\frac{7}{5} \cdot (x + 10))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{5}{7} (\frac{7}{5} x + \frac{7}{5} \cdot 10) = \frac{5}{7} (y - 8)$

Step 3.1.1.2

Combine $\frac{7}{5}$ and $x$ .

$\frac{5}{7} (\frac{7 x}{5} + \frac{7}{5} \cdot 10) = \frac{5}{7} (y - 8)$

Step 3.1.1.3

Cancel the common factor of $5$ .

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Step 3.1.1.3.1

Factor $5$ out of $10$ .

$\frac{5}{7} (\frac{7 x}{5} + \frac{7}{5} \cdot (5 (2))) = \frac{5}{7} (y - 8)$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{5}{7} (\frac{7 x}{5} + \frac{7}{5} \cdot (5 \cdot 2)) = \frac{5}{7} (y - 8)$

Step 3.1.1.3.3

Rewrite the expression.

$\frac{5}{7} (\frac{7 x}{5} + 7 \cdot 2) = \frac{5}{7} (y - 8)$

Step 3.1.1.4

Multiply $7$ by $2$ .

$\frac{5}{7} (\frac{7 x}{5} + 14) = \frac{5}{7} (y - 8)$

Step 3.1.1.5

Apply the distributive property.

$\frac{5}{7} \cdot \frac{7 x}{5} + \frac{5}{7} \cdot 14 = \frac{5}{7} (y - 8)$

Step 3.1.1.6

Cancel the common factor of $5$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{5}{7} \cdot \frac{7 x}{5} + \frac{5}{7} \cdot 14 = \frac{5}{7} (y - 8)$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{7} (7 x) + \frac{5}{7} \cdot 14 = \frac{5}{7} (y - 8)$

Step 3.1.1.7

Cancel the common factor of $7$ .

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Step 3.1.1.7.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) + \frac{5}{7} \cdot 14 = \frac{5}{7} (y - 8)$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{7} (7 x) + \frac{5}{7} \cdot 14 = \frac{5}{7} (y - 8)$

Step 3.1.1.7.3

Rewrite the expression.

$x + \frac{5}{7} \cdot 14 = \frac{5}{7} (y - 8)$

Step 3.1.1.8

Cancel the common factor of $7$ .

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Step 3.1.1.8.1

Factor $7$ out of $14$ .

$x + \frac{5}{7} \cdot (7 (2)) = \frac{5}{7} (y - 8)$

Step 3.1.1.8.2

Cancel the common factor.

$x + \frac{5}{7} \cdot (7 \cdot 2) = \frac{5}{7} (y - 8)$

Step 3.1.1.8.3

Rewrite the expression.

$x + 5 \cdot 2 = \frac{5}{7} (y - 8)$

Step 3.1.1.9

Multiply $5$ by $2$ .

$x + 10 = \frac{5}{7} (y - 8)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{7} (y - 8)$ .

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Step 3.2.1.1

Apply the distributive property.

$x + 10 = \frac{5}{7} y + \frac{5}{7} \cdot - 8$

Step 3.2.1.2

Combine $\frac{5}{7}$ and $y$ .

$x + 10 = \frac{5 y}{7} + \frac{5}{7} \cdot - 8$

Step 3.2.1.3

Multiply $\frac{5}{7} \cdot - 8$ .

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Step 3.2.1.3.1

Combine $\frac{5}{7}$ and $- 8$ .

$x + 10 = \frac{5 y}{7} + \frac{5 \cdot - 8}{7}$

Step 3.2.1.3.2

Multiply $5$ by $- 8$ .

$x + 10 = \frac{5 y}{7} + \frac{- 40}{7}$

Step 3.2.1.4

Move the negative in front of the fraction.

$x + 10 = \frac{5 y}{7} - \frac{40}{7}$

Step 4

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

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Step 4.1

Subtract $10$ from both sides of the equation.

$x = \frac{5 y}{7} - \frac{40}{7} - 10$

Step 4.2

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = \frac{5 y}{7} - \frac{40}{7} - 10 \cdot \frac{7}{7}$

Step 4.3

Combine $- 10$ and $\frac{7}{7}$ .

$x = \frac{5 y}{7} - \frac{40}{7} + \frac{- 10 \cdot 7}{7}$

Step 4.4

Combine the numerators over the common denominator.

$x = \frac{5 y}{7} + \frac{- 40 - 10 \cdot 7}{7}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 10$ by $7$ .

$x = \frac{5 y}{7} + \frac{- 40 - 70}{7}$

Step 4.5.2

Subtract $70$ from $- 40$ .

$x = \frac{5 y}{7} + \frac{- 110}{7}$

Step 4.6

Move the negative in front of the fraction.

$x = \frac{5 y}{7} - \frac{110}{7}$