Basic Math Examples

$y - (- 1) = (\frac{5}{6}) (y - 9)$

Step 1

Multiply $- 1$ by $- 1$ .

$y + 1 = \frac{5}{6} \cdot (y - 9)$

Step 2

Simplify $\frac{5}{6} \cdot (y - 9)$ .

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Step 2.1

Apply the distributive property.

$y + 1 = \frac{5}{6} y + \frac{5}{6} \cdot - 9$

Step 2.2

Combine $\frac{5}{6}$ and $y$ .

$y + 1 = \frac{5 y}{6} + \frac{5}{6} \cdot - 9$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $6$ .

$y + 1 = \frac{5 y}{6} + \frac{5}{3 (2)} \cdot - 9$

Step 2.3.2

Factor $3$ out of $- 9$ .

$y + 1 = \frac{5 y}{6} + \frac{5}{3 \cdot 2} \cdot (3 \cdot - 3)$

Step 2.3.3

Cancel the common factor.

$y + 1 = \frac{5 y}{6} + \frac{5}{3 \cdot 2} \cdot (3 \cdot - 3)$

Step 2.3.4

Rewrite the expression.

$y + 1 = \frac{5 y}{6} + \frac{5}{2} \cdot - 3$

Step 2.4

Combine $\frac{5}{2}$ and $- 3$ .

$y + 1 = \frac{5 y}{6} + \frac{5 \cdot - 3}{2}$

Step 2.5

Simplify the expression.

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Step 2.5.1

Multiply $5$ by $- 3$ .

$y + 1 = \frac{5 y}{6} + \frac{- 15}{2}$

Step 2.5.2

Move the negative in front of the fraction.

$y + 1 = \frac{5 y}{6} - \frac{15}{2}$

Step 3

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

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Step 3.1

Subtract $\frac{5 y}{6}$ from both sides of the equation.

$y + 1 - \frac{5 y}{6} = - \frac{15}{2}$

Step 3.2

To write $y$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y \cdot \frac{6}{6} - \frac{5 y}{6} + 1 = - \frac{15}{2}$

Step 3.3

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

$\frac{y \cdot 6}{6} - \frac{5 y}{6} + 1 = - \frac{15}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{y \cdot 6 - 5 y}{6} + 1 = - \frac{15}{2}$

Step 3.5

Subtract $5 y$ from $y \cdot 6$ .

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Step 3.5.1

Reorder $y$ and $6$ .

$\frac{6 \cdot y - 5 y}{6} + 1 = - \frac{15}{2}$

Step 3.5.2

Subtract $5 y$ from $6 \cdot y$ .

$\frac{y}{6} + 1 = - \frac{15}{2}$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$\frac{y}{6} = - \frac{15}{2} - 1$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{6} = - \frac{15}{2} - 1 \cdot \frac{2}{2}$

Step 4.3

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{y}{6} = - \frac{15}{2} + \frac{- 1 \cdot 2}{2}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{y}{6} = \frac{- 15 - 1 \cdot 2}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $2$ .

$\frac{y}{6} = \frac{- 15 - 2}{2}$

Step 4.5.2

Subtract $2$ from $- 15$ .

$\frac{y}{6} = \frac{- 17}{2}$

Step 4.6

Move the negative in front of the fraction.

$\frac{y}{6} = - \frac{17}{2}$

Step 5

Multiply both sides of the equation by $6$ .

$6 \frac{y}{6} = 6 (- \frac{17}{2})$

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

Cancel the common factor of $6$ .

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Step 6.1.1.1

Cancel the common factor.

$6 \frac{y}{6} = 6 (- \frac{17}{2})$

Step 6.1.1.2

Rewrite the expression.

$y = 6 (- \frac{17}{2})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $6 (- \frac{17}{2})$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{17}{2}$ into the numerator.

$y = 6 (\frac{- 17}{2})$

Step 6.2.1.1.2

Factor $2$ out of $6$ .

$y = 2 (3) \frac{- 17}{2}$

Step 6.2.1.1.3

Cancel the common factor.

$y = 2 \cdot 3 \frac{- 17}{2}$

Step 6.2.1.1.4

Rewrite the expression.

$y = 3 \cdot - 17$

Step 6.2.1.2

Multiply $3$ by $- 17$ .

$y = - 51$