Algebra Examples

$2 - \frac{1}{8} y = 11 + \frac{7}{8} y$

Step 1

Combine $y$ and $\frac{1}{8}$ .

$2 - \frac{y}{8} = 11 + \frac{7}{8} y$

Step 2

Combine $\frac{7}{8}$ and $y$ .

$2 - \frac{y}{8} = 11 + \frac{7 y}{8}$

Step 3

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

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Step 3.1

Subtract $\frac{7 y}{8}$ from both sides of the equation.

$2 - \frac{y}{8} - \frac{7 y}{8} = 11$

Step 3.2

Combine the numerators over the common denominator.

$2 + \frac{- y - 7 y}{8} = 11$

Step 3.3

Subtract $7 y$ from $- y$ .

$2 + \frac{- 8 y}{8} = 11$

Step 3.4

Cancel the common factor of $- 8$ and $8$ .

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Step 3.4.1

Factor $8$ out of $- 8 y$ .

$2 + \frac{8 (- y)}{8} = 11$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $8$ out of $8$ .

$2 + \frac{8 (- y)}{8 (1)} = 11$

Step 3.4.2.2

Cancel the common factor.

$2 + \frac{8 (- y)}{8 \cdot 1} = 11$

Step 3.4.2.3

Rewrite the expression.

$2 + \frac{- y}{1} = 11$

Step 3.4.2.4

Divide $- y$ by $1$ .

$2 - y = 11$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

$- y = 11 - 2$

Step 4.2

Subtract $2$ from $11$ .

$- y = 9$

Step 5

Divide each term in $- y = 9$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- y = 9$ by $- 1$ .

$\frac{- y}{- 1} = \frac{9}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{9}{- 1}$

Step 5.2.2

Divide $y$ by $1$ .

$y = \frac{9}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $9$ by $- 1$ .

$y = - 9$