Finite Math Examples

$8 = \frac{y + 9}{5} + \frac{7 y + 5}{2}$

Step 1

Rewrite the equation as $\frac{y + 9}{5} + \frac{7 y + 5}{2} = 8$ .

$\frac{y + 9}{5} + \frac{7 y + 5}{2} = 8$

Step 2

Simplify $\frac{y + 9}{5} + \frac{7 y + 5}{2}$ .

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Step 2.1

To write $\frac{y + 9}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y + 9}{5} \cdot \frac{2}{2} + \frac{7 y + 5}{2} = 8$

Step 2.2

To write $\frac{7 y + 5}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y + 9}{5} \cdot \frac{2}{2} + \frac{7 y + 5}{2} \cdot \frac{5}{5} = 8$

Step 2.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{y + 9}{5}$ by $\frac{2}{2}$ .

$\frac{(y + 9) \cdot 2}{5 \cdot 2} + \frac{7 y + 5}{2} \cdot \frac{5}{5} = 8$

Step 2.3.2

Multiply $5$ by $2$ .

$\frac{(y + 9) \cdot 2}{10} + \frac{7 y + 5}{2} \cdot \frac{5}{5} = 8$

Step 2.3.3

Multiply $\frac{7 y + 5}{2}$ by $\frac{5}{5}$ .

$\frac{(y + 9) \cdot 2}{10} + \frac{(7 y + 5) \cdot 5}{2 \cdot 5} = 8$

Step 2.3.4

Multiply $2$ by $5$ .

$\frac{(y + 9) \cdot 2}{10} + \frac{(7 y + 5) \cdot 5}{10} = 8$

Step 2.4

Combine the numerators over the common denominator.

$\frac{(y + 9) \cdot 2 + (7 y + 5) \cdot 5}{10} = 8$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{y \cdot 2 + 9 \cdot 2 + (7 y + 5) \cdot 5}{10} = 8$

Step 2.5.2

Move $2$ to the left of $y$ .

$\frac{2 \cdot y + 9 \cdot 2 + (7 y + 5) \cdot 5}{10} = 8$

Step 2.5.3

Multiply $9$ by $2$ .

$\frac{2 \cdot y + 18 + (7 y + 5) \cdot 5}{10} = 8$

Step 2.5.4

Apply the distributive property.

$\frac{2 y + 18 + 7 y \cdot 5 + 5 \cdot 5}{10} = 8$

Step 2.5.5

Multiply $5$ by $7$ .

$\frac{2 y + 18 + 35 y + 5 \cdot 5}{10} = 8$

Step 2.5.6

Multiply $5$ by $5$ .

$\frac{2 y + 18 + 35 y + 25}{10} = 8$

Step 2.5.7

Add $2 y$ and $35 y$ .

$\frac{37 y + 18 + 25}{10} = 8$

Step 2.5.8

Add $18$ and $25$ .

$\frac{37 y + 43}{10} = 8$

Step 3

Multiply both sides by $10$ .

$\frac{37 y + 43}{10} \cdot 10 = 8 \cdot 10$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{37 y + 43}{10} \cdot 10 = 8 \cdot 10$

Step 4.1.1.2

Rewrite the expression.

$37 y + 43 = 8 \cdot 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $8$ by $10$ .

$37 y + 43 = 80$

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

Subtract $43$ from both sides of the equation.

$37 y = 80 - 43$

Step 5.1.2

Subtract $43$ from $80$ .

$37 y = 37$

Step 5.2

Divide each term in $37 y = 37$ by $37$ and simplify.

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Step 5.2.1

Divide each term in $37 y = 37$ by $37$ .

$\frac{37 y}{37} = \frac{37}{37}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $37$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{37 y}{37} = \frac{37}{37}$

Step 5.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{37}{37}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $37$ by $37$ .

$y = 1$