Solve for y (2y)/5+2/6=y/2-1/6

$\frac{2 y}{5} + \frac{2}{6} = \frac{y}{2} - \frac{1}{6}$

Step 1

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$\frac{2 y}{5} + \frac{2 (1)}{6} = \frac{y}{2} - \frac{1}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 y}{5} + \frac{2 \cdot 1}{2 \cdot 3} = \frac{y}{2} - \frac{1}{6}$

Cancel the common factor.

$\frac{2 y}{5} + \frac{2 \cdot 1}{2 \cdot 3} = \frac{y}{2} - \frac{1}{6}$

Rewrite the expression.

$\frac{2 y}{5} + \frac{1}{3} = \frac{y}{2} - \frac{1}{6}$

Step 2

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

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

$\frac{2 y}{5} + \frac{1}{3} - \frac{y}{2} = - \frac{1}{6}$

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

$\frac{2 y}{5} \cdot \frac{2}{2} - \frac{y}{2} + \frac{1}{3} = - \frac{1}{6}$

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

$\frac{2 y}{5} \cdot \frac{2}{2} - \frac{y}{2} \cdot \frac{5}{5} + \frac{1}{3} = - \frac{1}{6}$

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

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

$\frac{2 y \cdot 2}{5 \cdot 2} - \frac{y}{2} \cdot \frac{5}{5} + \frac{1}{3} = - \frac{1}{6}$

Multiply $5$ by $2$ .

$\frac{2 y \cdot 2}{10} - \frac{y}{2} \cdot \frac{5}{5} + \frac{1}{3} = - \frac{1}{6}$

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

$\frac{2 y \cdot 2}{10} - \frac{y \cdot 5}{2 \cdot 5} + \frac{1}{3} = - \frac{1}{6}$

Multiply $2$ by $5$ .

$\frac{2 y \cdot 2}{10} - \frac{y \cdot 5}{10} + \frac{1}{3} = - \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{2 y \cdot 2 - y \cdot 5}{10} + \frac{1}{3} = - \frac{1}{6}$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $2 y \cdot 2 - y \cdot 5$ .

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

$\frac{y (2 \cdot 2) - y \cdot 5}{10} + \frac{1}{3} = - \frac{1}{6}$

Factor $y$ out of $- y \cdot 5$ .

$\frac{y (2 \cdot 2) + y (- 1 \cdot 5)}{10} + \frac{1}{3} = - \frac{1}{6}$

Factor $y$ out of $y (2 \cdot 2) + y (- 1 \cdot 5)$ .

$\frac{y (2 \cdot 2 - 1 \cdot 5)}{10} + \frac{1}{3} = - \frac{1}{6}$

Multiply $2$ by $2$ .

$\frac{y (4 - 1 \cdot 5)}{10} + \frac{1}{3} = - \frac{1}{6}$

Multiply $- 1$ by $5$ .

$\frac{y (4 - 5)}{10} + \frac{1}{3} = - \frac{1}{6}$

Subtract $5$ from $4$ .

$\frac{y \cdot - 1}{10} + \frac{1}{3} = - \frac{1}{6}$

Move $- 1$ to the left of $y$ .

$\frac{- 1 \cdot y}{10} + \frac{1}{3} = - \frac{1}{6}$

Move the negative in front of the fraction.

$- \frac{y}{10} + \frac{1}{3} = - \frac{1}{6}$

Step 3

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

Subtract $\frac{1}{3}$ from both sides of the equation.

$- \frac{y}{10} = - \frac{1}{6} - \frac{1}{3}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Multiply $3$ by $2$ .

$- \frac{y}{10} = - \frac{1}{6} - \frac{2}{6}$

Combine the numerators over the common denominator.

$- \frac{y}{10} = \frac{- 1 - 2}{6}$

Subtract $2$ from $- 1$ .

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

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

$- \frac{y}{10} = \frac{3 \cdot - 1}{3 \cdot 2}$

Cancel the common factor.

$- \frac{y}{10} = \frac{3 \cdot - 1}{3 \cdot 2}$

Rewrite the expression.

$- \frac{y}{10} = \frac{- 1}{2}$

Move the negative in front of the fraction.

$- \frac{y}{10} = - \frac{1}{2}$

Step 4

Multiply both sides of the equation by $- 10$ .

$- 10 (- \frac{y}{10}) = - 10 (- \frac{1}{2})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 10 (- \frac{y}{10})$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{y}{10}$ into the numerator.

$- 10 \frac{- y}{10} = - 10 (- \frac{1}{2})$

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- y}{10} = - 10 (- \frac{1}{2})$

Cancel the common factor.

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

Rewrite the expression.

$- - y = - 10 (- \frac{1}{2})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 10 (- \frac{1}{2})$

Multiply $y$ by $1$ .

$y = - 10 (- \frac{1}{2})$

Simplify the right side.

Simplify $- 10 (- \frac{1}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$y = - 10 (\frac{- 1}{2})$

Factor $2$ out of $- 10$ .

$y = 2 (- 5) \frac{- 1}{2}$

Cancel the common factor.

$y = 2 \cdot - 5 \frac{- 1}{2}$

Rewrite the expression.

$y = - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$y = 5$

Solve for y (2y)/5+2/6=y/2-1/6

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