Finite Math Examples

$y = \frac{6}{7} x + 385 + \frac{5}{7}$

Step 1

Rewrite the equation as $\frac{6}{7} x + 385 + \frac{5}{7} = y$ .

$\frac{6}{7} x + 385 + \frac{5}{7} = y$

Step 2

Simplify $\frac{6}{7} x + 385 + \frac{5}{7}$ .

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Step 2.1

Combine $\frac{6}{7}$ and $x$ .

$\frac{6 x}{7} + 385 + \frac{5}{7} = y$

Step 2.2

To write $385$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{6 x}{7} + 385 \cdot \frac{7}{7} + \frac{5}{7} = y$

Step 2.3

Combine $385$ and $\frac{7}{7}$ .

$\frac{6 x}{7} + \frac{385 \cdot 7}{7} + \frac{5}{7} = y$

Step 2.4

Combine the numerators over the common denominator.

$\frac{6 x}{7} + \frac{385 \cdot 7 + 5}{7} = y$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $385$ by $7$ .

$\frac{6 x}{7} + \frac{2695 + 5}{7} = y$

Step 2.5.2

Add $2695$ and $5$ .

$\frac{6 x}{7} + \frac{2700}{7} = y$

Step 3

Subtract $\frac{2700}{7}$ from both sides of the equation.

$\frac{6 x}{7} = y - \frac{2700}{7}$

Step 4

Multiply both sides of the equation by $\frac{7}{6}$ .

$\frac{7}{6} \cdot \frac{6 x}{7} = \frac{7}{6} (y - \frac{2700}{7})$

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 $\frac{7}{6} \cdot \frac{6 x}{7}$ .

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Step 5.1.1.1

Cancel the common factor of $7$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{7}{6} \cdot \frac{6 x}{7} = \frac{7}{6} (y - \frac{2700}{7})$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{6} (6 x) = \frac{7}{6} (y - \frac{2700}{7})$

Step 5.1.1.2

Cancel the common factor of $6$ .

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Step 5.1.1.2.1

Factor $6$ out of $6 x$ .

$\frac{1}{6} (6 (x)) = \frac{7}{6} (y - \frac{2700}{7})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{6} (6 x) = \frac{7}{6} (y - \frac{2700}{7})$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{7}{6} (y - \frac{2700}{7})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{7}{6} (y - \frac{2700}{7})$ .

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Step 5.2.1.1

Apply the distributive property.

$x = \frac{7}{6} y + \frac{7}{6} (- \frac{2700}{7})$

Step 5.2.1.2

Combine $\frac{7}{6}$ and $y$ .

$x = \frac{7 y}{6} + \frac{7}{6} (- \frac{2700}{7})$

Step 5.2.1.3

Cancel the common factor of $7$ .

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Step 5.2.1.3.1

Move the leading negative in $- \frac{2700}{7}$ into the numerator.

$x = \frac{7 y}{6} + \frac{7}{6} \cdot \frac{- 2700}{7}$

Step 5.2.1.3.2

Cancel the common factor.

$x = \frac{7 y}{6} + \frac{7}{6} \cdot \frac{- 2700}{7}$

Step 5.2.1.3.3

Rewrite the expression.

$x = \frac{7 y}{6} + \frac{1}{6} \cdot - 2700$

Step 5.2.1.4

Cancel the common factor of $6$ .

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Step 5.2.1.4.1

Factor $6$ out of $- 2700$ .

$x = \frac{7 y}{6} + \frac{1}{6} \cdot (6 (- 450))$

Step 5.2.1.4.2

Cancel the common factor.

$x = \frac{7 y}{6} + \frac{1}{6} \cdot (6 \cdot - 450)$

Step 5.2.1.4.3

Rewrite the expression.

$x = \frac{7 y}{6} - 450$