Finite Math Examples

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

Step 1

Simplify $2 (\frac{2}{3} - \frac{1}{3} y) - y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $y$ and $\frac{1}{3}$ .

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Multiply $2 (\frac{2}{3})$ .

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Step 1.1.3.1

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

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

Step 1.1.3.2

Multiply $2$ by $2$ .

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

Step 1.1.4

Multiply $2 (- \frac{y}{3})$ .

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Step 1.1.4.1

Multiply $- 1$ by $2$ .

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

Step 1.1.4.2

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

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

Step 1.1.5

Move the negative in front of the fraction.

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

Step 1.2

To write $- y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

Combine $- y$ and $\frac{3}{3}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Multiply $3$ by $- 1$ .

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

Step 1.7

Subtract $3 y$ from $- 2 y$ .

$\frac{4 - 5 y}{3} = 3$

Step 2

Multiply both sides by $3$ .

$\frac{4 - 5 y}{3} \cdot 3 = 3 \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{4 - 5 y}{3} \cdot 3$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{4 - 5 y}{3} \cdot 3 = 3 \cdot 3$

Step 3.1.1.1.2

Rewrite the expression.

$4 - 5 y = 3 \cdot 3$

Step 3.1.1.2

Reorder $4$ and $- 5 y$ .

$- 5 y + 4 = 3 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $3$ by $3$ .

$- 5 y + 4 = 9$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Subtract $4$ from both sides of the equation.

$- 5 y = 9 - 4$

Step 4.1.2

Subtract $4$ from $9$ .

$- 5 y = 5$

Step 4.2

Divide each term in $- 5 y = 5$ by $- 5$ and simplify.

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Step 4.2.1

Divide each term in $- 5 y = 5$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{5}{- 5}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 5$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{5}{- 5}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{- 5}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $5$ by $- 5$ .

$y = - 1$