Finite Math Examples

$\frac{3 y}{10} - 6 = \frac{y}{5} + 4$

Step 1

Move all terms containing $y$ to the left side of the equation.

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Step 1.1

Subtract $\frac{y}{5}$ from both sides of the equation.

$\frac{3 y}{10} - 6 - \frac{y}{5} = 4$

Step 1.2

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

$\frac{3 y}{10} - \frac{y}{5} \cdot \frac{2}{2} - 6 = 4$

Step 1.3

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

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Step 1.3.1

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

$\frac{3 y}{10} - \frac{y \cdot 2}{5 \cdot 2} - 6 = 4$

Step 1.3.2

Multiply $5$ by $2$ .

$\frac{3 y}{10} - \frac{y \cdot 2}{10} - 6 = 4$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 y - y \cdot 2}{10} - 6 = 4$

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Factor $y$ out of $3 y - y \cdot 2$ .

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Step 1.5.1.1.1

Factor $y$ out of $3 y$ .

$\frac{y \cdot 3 - y \cdot 2}{10} - 6 = 4$

Step 1.5.1.1.2

Factor $y$ out of $- y \cdot 2$ .

$\frac{y \cdot 3 + y (- 1 \cdot 2)}{10} - 6 = 4$

Step 1.5.1.1.3

Factor $y$ out of $y \cdot 3 + y (- 1 \cdot 2)$ .

$\frac{y (3 - 1 \cdot 2)}{10} - 6 = 4$

Step 1.5.1.2

Multiply $- 1$ by $2$ .

$\frac{y (3 - 2)}{10} - 6 = 4$

Step 1.5.1.3

Subtract $2$ from $3$ .

$\frac{y \cdot 1}{10} - 6 = 4$

Step 1.5.2

Multiply $y$ by $1$ .

$\frac{y}{10} - 6 = 4$

Step 2

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

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Step 2.1

Add $6$ to both sides of the equation.

$\frac{y}{10} = 4 + 6$

Step 2.2

Add $4$ and $6$ .

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

Step 3

Multiply both sides of the equation by $10$ .

$10 \frac{y}{10} = 10 \cdot 10$

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

Cancel the common factor of $10$ .

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Step 4.1.1.1

Cancel the common factor.

$10 \frac{y}{10} = 10 \cdot 10$

Step 4.1.1.2

Rewrite the expression.

$y = 10 \cdot 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $10$ by $10$ .

$y = 100$