Solve for y y/2=y/7+5

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

Multiply both sides of the equation by $2$ .

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

Simplify each term.

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

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

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

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

Multiply $5$ by $2$ .

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

Subtract $2 y$ from $7 y$ .

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

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

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

Simplify both sides of the equation.

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

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Cancel the common factor of $7$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

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Factor $5$ out of $5 y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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Cancel the common factor of $5$ .

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Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = 7 \cdot 2$

Multiply $7$ by $2$ .

$y = 14$

Solve for y y/2=y/7+5

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