Finite Math Examples

$- \frac{12}{5} + 3 y = 9$

Step 1

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

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Step 1.1

Add $\frac{12}{5}$ to both sides of the equation.

$3 y = 9 + \frac{12}{5}$

Step 1.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$3 y = 9 \cdot \frac{5}{5} + \frac{12}{5}$

Step 1.3

Combine $9$ and $\frac{5}{5}$ .

$3 y = \frac{9 \cdot 5}{5} + \frac{12}{5}$

Step 1.4

Combine the numerators over the common denominator.

$3 y = \frac{9 \cdot 5 + 12}{5}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $9$ by $5$ .

$3 y = \frac{45 + 12}{5}$

Step 1.5.2

Add $45$ and $12$ .

$3 y = \frac{57}{5}$

Step 2

Divide each term in $3 y = \frac{57}{5}$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 y = \frac{57}{5}$ by $3$ .

$\frac{3 y}{3} = \frac{\frac{57}{5}}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{\frac{57}{5}}{3}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{57}{5}}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{57}{5} \cdot \frac{1}{3}$

Step 2.3.2

Cancel the common factor of $3$ .

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Step 2.3.2.1

Factor $3$ out of $57$ .

$y = \frac{3 (19)}{5} \cdot \frac{1}{3}$

Step 2.3.2.2

Cancel the common factor.

$y = \frac{3 \cdot 19}{5} \cdot \frac{1}{3}$

Step 2.3.2.3

Rewrite the expression.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 3.8$

Mixed Number Form:

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