Finite Math Examples

$- 7 y + \frac{2}{3} = \frac{5}{3} y - \frac{7}{2}$

Step 1

Combine $\frac{5}{3}$ and $y$ .

$- 7 y + \frac{2}{3} = \frac{5 y}{3} - \frac{7}{2}$

Step 2

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

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Step 2.1

Subtract $\frac{5 y}{3}$ from both sides of the equation.

$- 7 y + \frac{2}{3} - \frac{5 y}{3} = - \frac{7}{2}$

Step 2.2

To write $- 7 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 7 y \cdot \frac{3}{3} - \frac{5 y}{3} + \frac{2}{3} = - \frac{7}{2}$

Step 2.3

Combine $- 7 y$ and $\frac{3}{3}$ .

$\frac{- 7 y \cdot 3}{3} - \frac{5 y}{3} + \frac{2}{3} = - \frac{7}{2}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 7 y \cdot 3 - 5 y}{3} + \frac{2}{3} = - \frac{7}{2}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 7 y \cdot 3 - 5 y + 2}{3} = - \frac{7}{2}$

Step 2.6

Multiply $3$ by $- 7$ .

$\frac{- 21 y - 5 y + 2}{3} = - \frac{7}{2}$

Step 2.7

Subtract $5 y$ from $- 21 y$ .

$\frac{- 26 y + 2}{3} = - \frac{7}{2}$

Step 2.8

Factor $2$ out of $- 26 y + 2$ .

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Step 2.8.1

Factor $2$ out of $- 26 y$ .

$\frac{2 (- 13 y) + 2}{3} = - \frac{7}{2}$

Step 2.8.2

Factor $2$ out of $2$ .

$\frac{2 (- 13 y) + 2 (1)}{3} = - \frac{7}{2}$

Step 2.8.3

Factor $2$ out of $2 (- 13 y) + 2 (1)$ .

$\frac{2 (- 13 y + 1)}{3} = - \frac{7}{2}$

Step 2.9

Factor $- 1$ out of $- 13 y$ .

$\frac{2 (- (13 y) + 1)}{3} = - \frac{7}{2}$

Step 2.10

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{2 (- (13 y) - 1 (- 1))}{3} = - \frac{7}{2}$

Step 2.11

Factor $- 1$ out of $- (13 y) - 1 (- 1)$ .

$\frac{2 (- (13 y - 1))}{3} = - \frac{7}{2}$

Step 2.12

Rewrite $- (13 y - 1)$ as $- 1 (13 y - 1)$ .

$\frac{2 (- 1 (13 y - 1))}{3} = - \frac{7}{2}$

Step 2.13

Move the negative in front of the fraction.

$- \frac{2 (13 y - 1)}{3} = - \frac{7}{2}$

Step 3

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

$- \frac{3}{2} (- \frac{2 (13 y - 1)}{3}) = - \frac{3}{2} (- \frac{7}{2})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{3}{2} (- \frac{2 (13 y - 1)}{3})$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} (- \frac{2 (13 y - 1)}{3}) = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.1.2

Move the leading negative in $- \frac{2 (13 y - 1)}{3}$ into the numerator.

$\frac{- 3}{2} \cdot \frac{- 2 (13 y - 1)}{3} = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 (13 y - 1)}{3} = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 (13 y - 1)}{3} = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 (13 y - 1)) = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $- 2 (13 y - 1)$ .

$\frac{- 1}{2} (2 (- (13 y - 1))) = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- (13 y - 1))) = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.2.3

Rewrite the expression.

$- - (13 y - 1) = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (13 y - 1) = - \frac{3}{2} (- \frac{7}{2})$

Step 4.1.1.3.2

Multiply $13 y - 1$ by $1$ .

$13 y - 1 = - \frac{3}{2} (- \frac{7}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{3}{2} (- \frac{7}{2})$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

$13 y - 1 = 1 (\frac{3}{2}) \frac{7}{2}$

Step 4.2.1.2

Multiply $\frac{3}{2}$ by $1$ .

$13 y - 1 = \frac{3}{2} \cdot \frac{7}{2}$

Step 4.2.1.3

Multiply $\frac{3}{2}$ by $\frac{7}{2}$ .

$13 y - 1 = \frac{3 \cdot 7}{2 \cdot 2}$

Step 4.2.1.4

Multiply $3$ by $7$ .

$13 y - 1 = \frac{21}{2 \cdot 2}$

Step 4.2.1.5

Multiply $2$ by $2$ .

$13 y - 1 = \frac{21}{4}$

Step 5

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

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Step 5.1

Add $1$ to both sides of the equation.

$13 y = \frac{21}{4} + 1$

Step 5.2

Write $1$ as a fraction with a common denominator.

$13 y = \frac{21}{4} + \frac{4}{4}$

Step 5.3

Combine the numerators over the common denominator.

$13 y = \frac{21 + 4}{4}$

Step 5.4

Add $21$ and $4$ .

$13 y = \frac{25}{4}$

Step 6

Divide each term in $13 y = \frac{25}{4}$ by $13$ and simplify.

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Step 6.1

Divide each term in $13 y = \frac{25}{4}$ by $13$ .

$\frac{13 y}{13} = \frac{\frac{25}{4}}{13}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $13$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{13 y}{13} = \frac{\frac{25}{4}}{13}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{25}{4}}{13}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{25}{4} \cdot \frac{1}{13}$

Step 6.3.2

Multiply $\frac{25}{4} \cdot \frac{1}{13}$ .

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Step 6.3.2.1

Multiply $\frac{25}{4}$ by $\frac{1}{13}$ .

$y = \frac{25}{4 \cdot 13}$

Step 6.3.2.2

Multiply $4$ by $13$ .

$y = \frac{25}{52}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{25}{52}$

Decimal Form:

$y = 0.48076923 \dots$