Finite Math Examples

$7 - y = \frac{1}{9} x - \frac{2}{9} + 7$

Step 1

Rewrite the equation as $\frac{1}{9} x - \frac{2}{9} + 7 = 7 - y$ .

$\frac{1}{9} x - \frac{2}{9} + 7 = 7 - y$

Step 2

Simplify $\frac{1}{9} x - \frac{2}{9} + 7$ .

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Step 2.1

Combine $\frac{1}{9}$ and $x$ .

$\frac{x}{9} - \frac{2}{9} + 7 = 7 - y$

Step 2.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{x}{9} - \frac{2}{9} + 7 \cdot \frac{9}{9} = 7 - y$

Step 2.3

Combine $7$ and $\frac{9}{9}$ .

$\frac{x}{9} - \frac{2}{9} + \frac{7 \cdot 9}{9} = 7 - y$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x}{9} + \frac{- 2 + 7 \cdot 9}{9} = 7 - y$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $9$ .

$\frac{x}{9} + \frac{- 2 + 63}{9} = 7 - y$

Step 2.5.2

Add $- 2$ and $63$ .

$\frac{x}{9} + \frac{61}{9} = 7 - y$

Step 3

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

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Step 3.1

Subtract $\frac{61}{9}$ from both sides of the equation.

$\frac{x}{9} = 7 - y - \frac{61}{9}$

Step 3.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{x}{9} = - y + 7 \cdot \frac{9}{9} - \frac{61}{9}$

Step 3.3

Combine $7$ and $\frac{9}{9}$ .

$\frac{x}{9} = - y + \frac{7 \cdot 9}{9} - \frac{61}{9}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x}{9} = - y + \frac{7 \cdot 9 - 61}{9}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $7$ by $9$ .

$\frac{x}{9} = - y + \frac{63 - 61}{9}$

Step 3.5.2

Subtract $61$ from $63$ .

$\frac{x}{9} = - y + \frac{2}{9}$

Step 4

Multiply both sides of the equation by $9$ .

$9 \frac{x}{9} = 9 (- y + \frac{2}{9})$

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

Cancel the common factor of $9$ .

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Step 5.1.1.1

Cancel the common factor.

$9 \frac{x}{9} = 9 (- y + \frac{2}{9})$

Step 5.1.1.2

Rewrite the expression.

$x = 9 (- y + \frac{2}{9})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $9 (- y + \frac{2}{9})$ .

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Step 5.2.1.1

Apply the distributive property.

$x = 9 (- y) + 9 (\frac{2}{9})$

Step 5.2.1.2

Multiply $- 1$ by $9$ .

$x = - 9 y + 9 (\frac{2}{9})$

Step 5.2.1.3

Cancel the common factor of $9$ .

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Step 5.2.1.3.1

Cancel the common factor.

$x = - 9 y + 9 (\frac{2}{9})$

Step 5.2.1.3.2

Rewrite the expression.

$x = - 9 y + 2$