Finite Math Examples

$5 (\frac{19}{3} + \frac{2}{3} y) + 5 = 5$

Step 1

Simplify $5 (\frac{19}{3} + \frac{2}{3} y) + 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$5 (\frac{19}{3} + \frac{2 y}{3}) + 5 = 5$

Step 1.1.2

Apply the distributive property.

$5 (\frac{19}{3}) + 5 \frac{2 y}{3} + 5 = 5$

Step 1.1.3

Multiply $5 (\frac{19}{3})$ .

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Step 1.1.3.1

Combine $5$ and $\frac{19}{3}$ .

$\frac{5 \cdot 19}{3} + 5 \frac{2 y}{3} + 5 = 5$

Step 1.1.3.2

Multiply $5$ by $19$ .

$\frac{95}{3} + 5 \frac{2 y}{3} + 5 = 5$

Step 1.1.4

Multiply $5 \frac{2 y}{3}$ .

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Step 1.1.4.1

Combine $5$ and $\frac{2 y}{3}$ .

$\frac{95}{3} + \frac{5 (2 y)}{3} + 5 = 5$

Step 1.1.4.2

Multiply $2$ by $5$ .

$\frac{95}{3} + \frac{10 y}{3} + 5 = 5$

Step 1.2

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

$\frac{10 y}{3} + \frac{95}{3} + 5 \cdot \frac{3}{3} = 5$

Step 1.3

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

$\frac{10 y}{3} + \frac{95}{3} + \frac{5 \cdot 3}{3} = 5$

Step 1.4

Combine the numerators over the common denominator.

$\frac{10 y}{3} + \frac{95 + 5 \cdot 3}{3} = 5$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $5$ by $3$ .

$\frac{10 y}{3} + \frac{95 + 15}{3} = 5$

Step 1.5.2

Add $95$ and $15$ .

$\frac{10 y}{3} + \frac{110}{3} = 5$

Step 2

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

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Step 2.1

Subtract $\frac{110}{3}$ from both sides of the equation.

$\frac{10 y}{3} = 5 - \frac{110}{3}$

Step 2.2

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

$\frac{10 y}{3} = 5 \cdot \frac{3}{3} - \frac{110}{3}$

Step 2.3

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

$\frac{10 y}{3} = \frac{5 \cdot 3}{3} - \frac{110}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{10 y}{3} = \frac{5 \cdot 3 - 110}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $5$ by $3$ .

$\frac{10 y}{3} = \frac{15 - 110}{3}$

Step 2.5.2

Subtract $110$ from $15$ .

$\frac{10 y}{3} = \frac{- 95}{3}$

Step 2.6

Move the negative in front of the fraction.

$\frac{10 y}{3} = - \frac{95}{3}$

Step 3

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

$10 y = - 95$

Step 4

Divide each term in $10 y = - 95$ by $10$ and simplify.

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Step 4.1

Divide each term in $10 y = - 95$ by $10$ .

$\frac{10 y}{10} = \frac{- 95}{10}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $10$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{- 95}{10}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 95}{10}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 95$ and $10$ .

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Step 4.3.1.1

Factor $5$ out of $- 95$ .

$y = \frac{5 (- 19)}{10}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $5$ out of $10$ .

$y = \frac{5 \cdot - 19}{5 \cdot 2}$

Step 4.3.1.2.2

Cancel the common factor.

$y = \frac{5 \cdot - 19}{5 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

$y = \frac{- 19}{2}$

Step 4.3.2

Move the negative in front of the fraction.

$y = - \frac{19}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{19}{2}$

Decimal Form:

$y = - 9.5$

Mixed Number Form:

$y = - 9 \frac{1}{2}$