Basic Math Examples

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{y}{7} + 5) \cdot 2$ .

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Step 2.2.1.1

Simplify terms.

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Step 2.2.1.1.1

Apply the distributive property.

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

Step 2.2.1.1.2

Combine $\frac{y}{7}$ and $2$ .

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

Step 2.2.1.1.3

Multiply $5$ by $2$ .

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

Step 2.2.1.2

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

$y = \frac{2 y}{7} + 10$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Subtract $\frac{2 y}{7}$ from both sides of the equation.

$y - \frac{2 y}{7} = 10$

Step 3.1.2

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

$y \cdot \frac{7}{7} - \frac{2 y}{7} = 10$

Step 3.1.3

Combine $y$ and $\frac{7}{7}$ .

$\frac{y \cdot 7}{7} - \frac{2 y}{7} = 10$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{y \cdot 7 - 2 y}{7} = 10$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Move $7$ to the left of $y$ .

$\frac{7 \cdot y - 2 y}{7} = 10$

Step 3.1.5.2

Subtract $2 y$ from $7 y$ .

$\frac{5 y}{7} = 10$

Step 3.2

Multiply both sides of the equation by $\frac{7}{5}$ .

$\frac{7}{5} \cdot \frac{5 y}{7} = \frac{7}{5} \cdot 10$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{7}{5} \cdot \frac{5 y}{7}$ .

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Step 3.3.1.1.1

Cancel the common factor of $7$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{7}{5} \cdot \frac{5 y}{7} = \frac{7}{5} \cdot 10$

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 y) = \frac{7}{5} \cdot 10$

Step 3.3.1.1.2

Cancel the common factor of $5$ .

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Step 3.3.1.1.2.1

Factor $5$ out of $5 y$ .

$\frac{1}{5} (5 (y)) = \frac{7}{5} \cdot 10$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 y) = \frac{7}{5} \cdot 10$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = \frac{7}{5} \cdot 10$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{7}{5} \cdot 10$ .

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Step 3.3.2.1.1

Cancel the common factor of $5$ .

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Step 3.3.2.1.1.1

Factor $5$ out of $10$ .

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

Step 3.3.2.1.1.2

Cancel the common factor.

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

Step 3.3.2.1.1.3

Rewrite the expression.

$y = 7 \cdot 2$

Step 3.3.2.1.2

Multiply $7$ by $2$ .

$y = 14$