Basic Math Examples

$\frac{4}{9} y + 5 = - \frac{7}{9} y - 8$

Step 1

Combine $\frac{4}{9}$ and $y$ .

$\frac{4 y}{9} + 5 = - \frac{7}{9} y - 8$

Step 2

Simplify each term.

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Step 2.1

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

$\frac{4 y}{9} + 5 = - \frac{y \cdot 7}{9} - 8$

Step 2.2

Move $7$ to the left of $y$ .

$\frac{4 y}{9} + 5 = - \frac{7 y}{9} - 8$

Step 3

Move all terms containing $y$ to the left side of the equation.

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Step 3.1

Add $\frac{7 y}{9}$ to both sides of the equation.

$\frac{4 y}{9} + 5 + \frac{7 y}{9} = - 8$

Step 3.2

Combine the numerators over the common denominator.

$5 + \frac{4 y + 7 y}{9} = - 8$

Step 3.3

Add $4 y$ and $7 y$ .

$5 + \frac{11 y}{9} = - 8$

Step 4

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

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Step 4.1

Subtract $5$ from both sides of the equation.

$\frac{11 y}{9} = - 8 - 5$

Step 4.2

Subtract $5$ from $- 8$ .

$\frac{11 y}{9} = - 13$

Step 5

Multiply both sides of the equation by $\frac{9}{11}$ .

$\frac{9}{11} \cdot \frac{11 y}{9} = \frac{9}{11} \cdot - 13$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{9}{11} \cdot \frac{11 y}{9}$ .

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Step 6.1.1.1

Cancel the common factor of $9$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{9}{11} \cdot \frac{11 y}{9} = \frac{9}{11} \cdot - 13$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 y) = \frac{9}{11} \cdot - 13$

Step 6.1.1.2

Cancel the common factor of $11$ .

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Step 6.1.1.2.1

Factor $11$ out of $11 y$ .

$\frac{1}{11} (11 (y)) = \frac{9}{11} \cdot - 13$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 y) = \frac{9}{11} \cdot - 13$

Step 6.1.1.2.3

Rewrite the expression.

$y = \frac{9}{11} \cdot - 13$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{9}{11} \cdot - 13$ .

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Step 6.2.1.1

Multiply $\frac{9}{11} \cdot - 13$ .

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Step 6.2.1.1.1

Combine $\frac{9}{11}$ and $- 13$ .

$y = \frac{9 \cdot - 13}{11}$

Step 6.2.1.1.2

Multiply $9$ by $- 13$ .

$y = \frac{- 117}{11}$

Step 6.2.1.2

Move the negative in front of the fraction.

$y = - \frac{117}{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{117}{11}$

Decimal Form:

$y = - 10.\overline{63}$

Mixed Number Form:

$y = - 10 \frac{7}{11}$