Finite Math Examples

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(4 - \frac{y}{6}) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$y = 4 \cdot 3 - \frac{y}{6} \cdot 3$

Step 2.2.1.2

Multiply $4$ by $3$ .

$y = 12 - \frac{y}{6} \cdot 3$

Step 2.2.1.3

Cancel the common factor of $3$ .

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Step 2.2.1.3.1

Move the leading negative in $- \frac{y}{6}$ into the numerator.

$y = 12 + \frac{- y}{6} \cdot 3$

Step 2.2.1.3.2

Factor $3$ out of $6$ .

$y = 12 + \frac{- y}{3 (2)} \cdot 3$

Step 2.2.1.3.3

Cancel the common factor.

$y = 12 + \frac{- y}{3 \cdot 2} \cdot 3$

Step 2.2.1.3.4

Rewrite the expression.

$y = 12 + \frac{- y}{2}$

Step 2.2.1.4

Simplify the expression.

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Step 2.2.1.4.1

Move the negative in front of the fraction.

$y = 12 - \frac{y}{2}$

Step 2.2.1.4.2

Reorder $12$ and $- \frac{y}{2}$ .

$y = - \frac{y}{2} + 12$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Add $\frac{y}{2}$ to both sides of the equation.

$y + \frac{y}{2} = 12$

Step 3.1.2

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

$y \cdot \frac{2}{2} + \frac{y}{2} = 12$

Step 3.1.3

Combine $y$ and $\frac{2}{2}$ .

$\frac{y \cdot 2}{2} + \frac{y}{2} = 12$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{y \cdot 2 + y}{2} = 12$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Move $2$ to the left of $y$ .

$\frac{2 \cdot y + y}{2} = 12$

Step 3.1.5.2

Add $2 y$ and $y$ .

$\frac{3 y}{2} = 12$

Step 3.2

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 y}{2} = \frac{2}{3} \cdot 12$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

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

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Step 3.3.1.1.1

Cancel the common factor of $2$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 y}{2} = \frac{2}{3} \cdot 12$

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 y) = \frac{2}{3} \cdot 12$

Step 3.3.1.1.2

Cancel the common factor of $3$ .

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Step 3.3.1.1.2.1

Factor $3$ out of $3 y$ .

$\frac{1}{3} (3 (y)) = \frac{2}{3} \cdot 12$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 y) = \frac{2}{3} \cdot 12$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = \frac{2}{3} \cdot 12$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{2}{3} \cdot 12$ .

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Step 3.3.2.1.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1.1

Factor $3$ out of $12$ .

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

Step 3.3.2.1.1.2

Cancel the common factor.

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

Step 3.3.2.1.1.3

Rewrite the expression.

$y = 2 \cdot 4$

Step 3.3.2.1.2

Multiply $2$ by $4$ .

$y = 8$