Finite Math Examples

$\frac{1}{3} \cdot (9 - 12 y) + \frac{1}{5} y = - \frac{4}{5}$

Step 1

Simplify $\frac{1}{3} \cdot (9 - 12 y) + \frac{1}{5} y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{3} \cdot 9 + \frac{1}{3} (- 12 y) + \frac{1}{5} y = - \frac{4}{5}$

Step 1.1.2

Cancel the common factor of $3$ .

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Step 1.1.2.1

Factor $3$ out of $9$ .

$\frac{1}{3} \cdot (3 (3)) + \frac{1}{3} (- 12 y) + \frac{1}{5} y = - \frac{4}{5}$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 3) + \frac{1}{3} (- 12 y) + \frac{1}{5} y = - \frac{4}{5}$

Step 1.1.2.3

Rewrite the expression.

$3 + \frac{1}{3} (- 12 y) + \frac{1}{5} y = - \frac{4}{5}$

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

Factor $3$ out of $- 12 y$ .

$3 + \frac{1}{3} (3 (- 4 y)) + \frac{1}{5} y = - \frac{4}{5}$

Step 1.1.3.2

Cancel the common factor.

$3 + \frac{1}{3} (3 (- 4 y)) + \frac{1}{5} y = - \frac{4}{5}$

Step 1.1.3.3

Rewrite the expression.

$3 - 4 y + \frac{1}{5} y = - \frac{4}{5}$

Step 1.1.4

Combine $\frac{1}{5}$ and $y$ .

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

Step 1.2

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

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

Step 1.3

Simplify terms.

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Step 1.3.1

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

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

Step 1.3.2

Combine the numerators over the common denominator.

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

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $y$ out of $- 4 y \cdot 5 + y$ .

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Step 1.4.1.1.1

Factor $y$ out of $- 4 y \cdot 5$ .

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

Step 1.4.1.1.2

Raise $y$ to the power of $1$ .

$3 + \frac{y (- 4 \cdot 5) + y^{1}}{5} = - \frac{4}{5}$

Step 1.4.1.1.3

Factor $y$ out of $y^{1}$ .

$3 + \frac{y (- 4 \cdot 5) + y \cdot 1}{5} = - \frac{4}{5}$

Step 1.4.1.1.4

Factor $y$ out of $y (- 4 \cdot 5) + y \cdot 1$ .

$3 + \frac{y (- 4 \cdot 5 + 1)}{5} = - \frac{4}{5}$

Step 1.4.1.2

Multiply $- 4$ by $5$ .

$3 + \frac{y (- 20 + 1)}{5} = - \frac{4}{5}$

Step 1.4.1.3

Add $- 20$ and $1$ .

$3 + \frac{y \cdot - 19}{5} = - \frac{4}{5}$

Step 1.4.2

Move $- 19$ to the left of $y$ .

$3 + \frac{- 19 \cdot y}{5} = - \frac{4}{5}$

Step 1.4.3

Move the negative in front of the fraction.

$3 - \frac{19 y}{5} = - \frac{4}{5}$

Step 2

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

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Step 2.1

Subtract $3$ from both sides of the equation.

$- \frac{19 y}{5} = - \frac{4}{5} - 3$

Step 2.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{19 y}{5} = - \frac{4}{5} - 3 \cdot \frac{5}{5}$

Step 2.3

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

$- \frac{19 y}{5} = - \frac{4}{5} + \frac{- 3 \cdot 5}{5}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{19 y}{5} = \frac{- 4 - 3 \cdot 5}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 3$ by $5$ .

$- \frac{19 y}{5} = \frac{- 4 - 15}{5}$

Step 2.5.2

Subtract $15$ from $- 4$ .

$- \frac{19 y}{5} = \frac{- 19}{5}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{19 y}{5} = - \frac{19}{5}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 19 y = - 19$

Step 4

Divide each term in $- 19 y = - 19$ by $- 19$ and simplify.

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Step 4.1

Divide each term in $- 19 y = - 19$ by $- 19$ .

$\frac{- 19 y}{- 19} = \frac{- 19}{- 19}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 19$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 19 y}{- 19} = \frac{- 19}{- 19}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 19}{- 19}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 19$ by $- 19$ .

$y = 1$