Finite Math Examples

$(5 + \frac{y}{2}) + y = 41$

Step 1

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

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Step 1.1

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

$5 + \frac{y}{2} + y \cdot \frac{2}{2} = 41$

Step 1.2

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

$5 + \frac{y}{2} + \frac{y \cdot 2}{2} = 41$

Step 1.3

Combine the numerators over the common denominator.

$5 + \frac{y + y \cdot 2}{2} = 41$

Step 1.4

Add $y$ and $y \cdot 2$ .

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Step 1.4.1

Reorder $y$ and $2$ .

$5 + \frac{y + 2 \cdot y}{2} = 41$

Step 1.4.2

Add $y$ and $2 \cdot y$ .

$5 + \frac{3 y}{2} = 41$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$\frac{3 y}{2} = 41 - 5$

Step 2.2

Subtract $5$ from $41$ .

$\frac{3 y}{2} = 36$

Step 3

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 y}{2} = \frac{2}{3} \cdot 36$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{2}{3} \cdot \frac{3 y}{2}$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 y}{2} = \frac{2}{3} \cdot 36$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 y) = \frac{2}{3} \cdot 36$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $3 y$ .

$\frac{1}{3} (3 (y)) = \frac{2}{3} \cdot 36$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 y) = \frac{2}{3} \cdot 36$

Step 4.1.1.2.3

Rewrite the expression.

$y = \frac{2}{3} \cdot 36$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{3} \cdot 36$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Factor $3$ out of $36$ .

$y = \frac{2}{3} \cdot (3 (12))$

Step 4.2.1.1.2

Cancel the common factor.

$y = \frac{2}{3} \cdot (3 \cdot 12)$

Step 4.2.1.1.3

Rewrite the expression.

$y = 2 \cdot 12$

Step 4.2.1.2

Multiply $2$ by $12$ .

$y = 24$