Finite Math Examples

$2 y - \frac{4}{3} = - \frac{4}{3} y - \frac{3}{5}$

Step 1

Simplify each term.

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Step 1.1

Combine $y$ and $\frac{4}{3}$ .

$2 y - \frac{4}{3} = - \frac{y \cdot 4}{3} - \frac{3}{5}$

Step 1.2

Move $4$ to the left of $y$ .

$2 y - \frac{4}{3} = - \frac{4 y}{3} - \frac{3}{5}$

Step 2

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

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Step 2.1

Add $\frac{4 y}{3}$ to both sides of the equation.

$2 y - \frac{4}{3} + \frac{4 y}{3} = - \frac{3}{5}$

Step 2.2

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

$2 y \cdot \frac{3}{3} + \frac{4 y}{3} - \frac{4}{3} = - \frac{3}{5}$

Step 2.3

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

$\frac{2 y \cdot 3}{3} + \frac{4 y}{3} - \frac{4}{3} = - \frac{3}{5}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 y \cdot 3 + 4 y}{3} - \frac{4}{3} = - \frac{3}{5}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{2 y \cdot 3 + 4 y - 4}{3} = - \frac{3}{5}$

Step 2.6

Multiply $3$ by $2$ .

$\frac{6 y + 4 y - 4}{3} = - \frac{3}{5}$

Step 2.7

Add $6 y$ and $4 y$ .

$\frac{10 y - 4}{3} = - \frac{3}{5}$

Step 2.8

Factor $2$ out of $10 y - 4$ .

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Step 2.8.1

Factor $2$ out of $10 y$ .

$\frac{2 (5 y) - 4}{3} = - \frac{3}{5}$

Step 2.8.2

Factor $2$ out of $- 4$ .

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

Step 2.8.3

Factor $2$ out of $2 (5 y) + 2 (- 2)$ .

$\frac{2 (5 y - 2)}{3} = - \frac{3}{5}$

Step 3

Multiply both sides by $3$ .

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

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{2 (5 y - 2)}{3} \cdot 3$ .

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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

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Apply the distributive property.

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

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $5$ by $2$ .

$10 y + 2 \cdot - 2 = - \frac{3}{5} \cdot 3$

Step 4.1.1.3.2

Multiply $2$ by $- 2$ .

$10 y - 4 = - \frac{3}{5} \cdot 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

Multiply $- \frac{3}{5} \cdot 3$ .

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Step 4.2.1.1.1

Multiply $3$ by $- 1$ .

$10 y - 4 = - 3 (\frac{3}{5})$

Step 4.2.1.1.2

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

$10 y - 4 = \frac{- 3 \cdot 3}{5}$

Step 4.2.1.1.3

Multiply $- 3$ by $3$ .

$10 y - 4 = \frac{- 9}{5}$

Step 4.2.1.2

Move the negative in front of the fraction.

$10 y - 4 = - \frac{9}{5}$

Step 5

Solve for $y$ .

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Step 5.1

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

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Step 5.1.1

Add $4$ to both sides of the equation.

$10 y = - \frac{9}{5} + 4$

Step 5.1.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$10 y = - \frac{9}{5} + 4 \cdot \frac{5}{5}$

Step 5.1.3

Combine $4$ and $\frac{5}{5}$ .

$10 y = - \frac{9}{5} + \frac{4 \cdot 5}{5}$

Step 5.1.4

Combine the numerators over the common denominator.

$10 y = \frac{- 9 + 4 \cdot 5}{5}$

Step 5.1.5

Simplify the numerator.

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Step 5.1.5.1

Multiply $4$ by $5$ .

$10 y = \frac{- 9 + 20}{5}$

Step 5.1.5.2

Add $- 9$ and $20$ .

$10 y = \frac{11}{5}$

Step 5.2

Divide each term in $10 y = \frac{11}{5}$ by $10$ and simplify.

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Step 5.2.1

Divide each term in $10 y = \frac{11}{5}$ by $10$ .

$\frac{10 y}{10} = \frac{\frac{11}{5}}{10}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $10$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{\frac{11}{5}}{10}$

Step 5.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{11}{5}}{10}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{11}{5} \cdot \frac{1}{10}$

Step 5.2.3.2

Multiply $\frac{11}{5} \cdot \frac{1}{10}$ .

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Step 5.2.3.2.1

Multiply $\frac{11}{5}$ by $\frac{1}{10}$ .

$y = \frac{11}{5 \cdot 10}$

Step 5.2.3.2.2

Multiply $5$ by $10$ .

$y = \frac{11}{50}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{11}{50}$

Decimal Form:

$y = 0.22$