Finite Math Examples

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

Step 1

Simplify.

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Step 1.1

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

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

Step 1.2

Multiply $2$ by $1$ .

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

Step 2

Divide each term in $2 (\frac{2}{3} - \frac{y}{3}) = 3$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 (\frac{2}{3} - \frac{y}{3}) = 3$ by $2$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $\frac{2}{3} - \frac{y}{3}$ by $1$ .

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

Step 3

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

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Step 3.1

Subtract $\frac{2}{3}$ from both sides of the equation.

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

Step 3.2

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{3}{2}$ by $\frac{3}{3}$ .

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

Step 3.4.2

Multiply $2$ by $3$ .

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

Step 3.4.3

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

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

Step 3.4.4

Multiply $3$ by $2$ .

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $3$ by $3$ .

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

Step 3.6.2

Multiply $- 2$ by $2$ .

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

Step 3.6.3

Subtract $4$ from $9$ .

$- \frac{y}{3} = \frac{5}{6}$

Step 4

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{y}{3}) = - 3 (\frac{5}{6})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$- 3 \frac{- y}{3} = - 3 (\frac{5}{6})$

Step 5.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 5.1.1.1.3

Cancel the common factor.

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

Step 5.1.1.1.4

Rewrite the expression.

$- - y = - 3 (\frac{5}{6})$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 5.1.1.2.2

Multiply $y$ by $1$ .

$y = - 3 (\frac{5}{6})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Factor $3$ out of $- 3$ .

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

Step 5.2.1.2

Factor $3$ out of $6$ .

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

Step 5.2.1.3

Cancel the common factor.

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

Step 5.2.1.4

Rewrite the expression.

$y = - \frac{5}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{5}{2}$

Decimal Form:

$y = - 2.5$

Mixed Number Form:

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