Algebra Examples

$\frac{3 y - 6}{9} = \frac{4 - 2 y}{- 3}$

Step 1

Cancel the common factor of $3 y - 6$ and $9$ .

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Step 1.1

Factor $3$ out of $3 y$ .

$\frac{3 (y) - 6}{9} = \frac{4 - 2 y}{- 3}$

Step 1.2

Factor $3$ out of $- 6$ .

$\frac{3 y + 3 \cdot - 2}{9} = \frac{4 - 2 y}{- 3}$

Step 1.3

Factor $3$ out of $3 y + 3 \cdot - 2$ .

$\frac{3 (y - 2)}{9} = \frac{4 - 2 y}{- 3}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $9$ .

$\frac{3 (y - 2)}{3 (3)} = \frac{4 - 2 y}{- 3}$

Step 1.4.2

Cancel the common factor.

$\frac{3 (y - 2)}{3 \cdot 3} = \frac{4 - 2 y}{- 3}$

Step 1.4.3

Rewrite the expression.

$\frac{y - 2}{3} = \frac{4 - 2 y}{- 3}$

Step 2

Multiply both sides by $3$ .

$\frac{y - 2}{3} \cdot 3 = \frac{4 - 2 y}{- 3} \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{y - 2}{3} \cdot 3 = \frac{4 - 2 y}{- 3} \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$y - 2 = \frac{4 - 2 y}{- 3} \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{4 - 2 y}{- 3} \cdot 3$ .

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Step 3.2.1.1

Factor $2$ out of $4 - 2 y$ .

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Step 3.2.1.1.1

Factor $2$ out of $4$ .

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

Step 3.2.1.1.2

Factor $2$ out of $- 2 y$ .

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

Step 3.2.1.1.3

Factor $2$ out of $2 (2) + 2 (- y)$ .

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

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Factor $3$ out of $- 3$ .

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

Step 3.2.1.2.2

Cancel the common factor.

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

Step 3.2.1.2.3

Rewrite the expression.

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

Step 3.2.1.3

Simplify the expression.

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Step 3.2.1.3.1

Move the negative one from the denominator of $\frac{2 (2 - y)}{- 1}$ .

$y - 2 = - 1 \cdot (2 (2 - y))$

Step 3.2.1.3.2

Rewrite $- 1 \cdot (2 (2 - y))$ as $- (2 (2 - y))$ .

$y - 2 = - (2 (2 - y))$

Step 3.2.1.4

Apply the distributive property.

$y - 2 = - (2 \cdot 2 + 2 (- y))$

Step 3.2.1.5

Multiply.

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Step 3.2.1.5.1

Multiply $2$ by $2$ .

$y - 2 = - (4 + 2 (- y))$

Step 3.2.1.5.2

Multiply $- 1$ by $2$ .

$y - 2 = - (4 - 2 y)$

Step 3.2.1.6

Apply the distributive property.

$y - 2 = - 1 \cdot 4 - (- 2 y)$

Step 3.2.1.7

Simplify the expression.

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Step 3.2.1.7.1

Multiply $- 1$ by $4$ .

$y - 2 = - 4 - (- 2 y)$

Step 3.2.1.7.2

Multiply $- 2$ by $- 1$ .

$y - 2 = - 4 + 2 y$

Step 3.2.1.7.3

Reorder $- 4$ and $2 y$ .

$y - 2 = 2 y - 4$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Subtract $2 y$ from both sides of the equation.

$y - 2 - 2 y = - 4$

Step 4.1.2

Subtract $2 y$ from $y$ .

$- y - 2 = - 4$

Step 4.2

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

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Step 4.2.1

Add $2$ to both sides of the equation.

$- y = - 4 + 2$

Step 4.2.2

Add $- 4$ and $2$ .

$- y = - 2$

Step 4.3

Divide each term in $- y = - 2$ by $- 1$ and simplify.

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Step 4.3.1

Divide each term in $- y = - 2$ by $- 1$ .

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Dividing two negative values results in a positive value.

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

Step 4.3.2.2

Divide $y$ by $1$ .

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

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 2$ by $- 1$ .

$y = 2$