Finite Math Examples

$\frac{4 y - 10}{3} + \frac{6 y + 8}{2} = 9$

Step 1

Simplify $\frac{4 y - 10}{3} + \frac{6 y + 8}{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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Step 1.1.1.1

Factor $2$ out of $4 y$ .

$\frac{2 (2 y) - 10}{3} + \frac{6 y + 8}{2} = 9$

Step 1.1.1.2

Factor $2$ out of $- 10$ .

$\frac{2 (2 y) + 2 (- 5)}{3} + \frac{6 y + 8}{2} = 9$

Step 1.1.1.3

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

$\frac{2 (2 y - 5)}{3} + \frac{6 y + 8}{2} = 9$

Step 1.1.2

Cancel the common factor of $6 y + 8$ and $2$ .

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Step 1.1.2.1

Factor $2$ out of $6 y$ .

$\frac{2 (2 y - 5)}{3} + \frac{2 (3 y) + 8}{2} = 9$

Step 1.1.2.2

Factor $2$ out of $8$ .

$\frac{2 (2 y - 5)}{3} + \frac{2 (3 y) + 2 \cdot 4}{2} = 9$

Step 1.1.2.3

Factor $2$ out of $2 (3 y) + 2 (4)$ .

$\frac{2 (2 y - 5)}{3} + \frac{2 (3 y + 4)}{2} = 9$

Step 1.1.2.4

Cancel the common factors.

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Step 1.1.2.4.1

Factor $2$ out of $2$ .

$\frac{2 (2 y - 5)}{3} + \frac{2 (3 y + 4)}{2 (1)} = 9$

Step 1.1.2.4.2

Cancel the common factor.

$\frac{2 (2 y - 5)}{3} + \frac{2 (3 y + 4)}{2 \cdot 1} = 9$

Step 1.1.2.4.3

Rewrite the expression.

$\frac{2 (2 y - 5)}{3} + \frac{3 y + 4}{1} = 9$

Step 1.1.2.4.4

Divide $3 y + 4$ by $1$ .

$\frac{2 (2 y - 5)}{3} + 3 y + 4 = 9$

Step 1.2

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

$\frac{2 (2 y - 5)}{3} + 3 y \cdot \frac{3}{3} + 4 = 9$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{2 (2 y - 5)}{3} + \frac{3 y \cdot 3}{3} + 4 = 9$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{2 (2 y - 5) + 3 y \cdot 3}{3} + 4 = 9$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the distributive property.

$\frac{2 (2 y) + 2 \cdot - 5 + 3 y \cdot 3}{3} + 4 = 9$

Step 1.4.2

Multiply $2$ by $2$ .

$\frac{4 y + 2 \cdot - 5 + 3 y \cdot 3}{3} + 4 = 9$

Step 1.4.3

Multiply $2$ by $- 5$ .

$\frac{4 y - 10 + 3 y \cdot 3}{3} + 4 = 9$

Step 1.4.4

Multiply $3$ by $3$ .

$\frac{4 y - 10 + 9 y}{3} + 4 = 9$

Step 1.4.5

Add $4 y$ and $9 y$ .

$\frac{13 y - 10}{3} + 4 = 9$

Step 1.5

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{13 y - 10}{3} + 4 \cdot \frac{3}{3} = 9$

Step 1.6

Simplify terms.

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Step 1.6.1

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

$\frac{13 y - 10}{3} + \frac{4 \cdot 3}{3} = 9$

Step 1.6.2

Combine the numerators over the common denominator.

$\frac{13 y - 10 + 4 \cdot 3}{3} = 9$

Step 1.7

Simplify the numerator.

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Step 1.7.1

Multiply $4$ by $3$ .

$\frac{13 y - 10 + 12}{3} = 9$

Step 1.7.2

Add $- 10$ and $12$ .

$\frac{13 y + 2}{3} = 9$

Step 2

Multiply both sides by $3$ .

$\frac{13 y + 2}{3} \cdot 3 = 9 \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{13 y + 2}{3} \cdot 3 = 9 \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$13 y + 2 = 9 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $9$ by $3$ .

$13 y + 2 = 27$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Subtract $2$ from both sides of the equation.

$13 y = 27 - 2$

Step 4.1.2

Subtract $2$ from $27$ .

$13 y = 25$

Step 4.2

Divide each term in $13 y = 25$ by $13$ and simplify.

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Step 4.2.1

Divide each term in $13 y = 25$ by $13$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $13$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $y$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 1.\overline{923076}$

Mixed Number Form:

$y = 1 \frac{12}{13}$