Solve for y 1/12+3/8y=5/12+5/8y

$\frac{1}{12} + \frac{3}{8} y = \frac{5}{12} + \frac{5}{8} y$

Combine $\frac{3}{8}$ and $y$ .

$\frac{1}{12} + \frac{3 y}{8} = \frac{5}{12} + \frac{5}{8} y$

Combine $\frac{5}{8}$ and $y$ .

$\frac{1}{12} + \frac{3 y}{8} = \frac{5}{12} + \frac{5 y}{8}$

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

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Subtract $\frac{5 y}{8}$ from both sides of the equation.

$\frac{1}{12} + \frac{3 y}{8} - \frac{5 y}{8} = \frac{5}{12}$

Combine fractions with similar denominators.

$\frac{1}{12} + \frac{3 y - 5 y}{8} = \frac{5}{12}$

Subtract $5 y$ from $3 y$ .

$\frac{1}{12} + \frac{- 2 y}{8} = \frac{5}{12}$

Reduce the expression $\frac{- 2 y}{8}$ by cancelling the common factors.

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

$\frac{1}{12} + \frac{2 (- y)}{8} = \frac{5}{12}$

Factor $2$ out of $8$ .

$\frac{1}{12} + \frac{2 (- y)}{2 (4)} = \frac{5}{12}$

Cancel the common factor.

$\frac{1}{12} + \frac{2 (- y)}{2 \cdot 4} = \frac{5}{12}$

Rewrite the expression.

$\frac{1}{12} + \frac{- y}{4} = \frac{5}{12}$

Move the negative in front of the fraction.

$\frac{1}{12} - \frac{y}{4} = \frac{5}{12}$

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

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Subtract $\frac{1}{12}$ from both sides of the equation.

$- \frac{y}{4} = \frac{5}{12} - \frac{1}{12}$

Combine the numerators over the common denominator.

$- \frac{y}{4} = \frac{5 - 1}{12}$

Subtract $1$ from $5$ .

$- \frac{y}{4} = \frac{4}{12}$

Cancel the common factor of $4$ and $12$ .

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Factor $4$ out of $4$ .

$- \frac{y}{4} = \frac{4 (1)}{12}$

Cancel the common factors.

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Factor $4$ out of $12$ .

$- \frac{y}{4} = \frac{4 \cdot 1}{4 \cdot 3}$

Cancel the common factor.

$- \frac{y}{4} = \frac{4 \cdot 1}{4 \cdot 3}$

Rewrite the expression.

$- \frac{y}{4} = \frac{1}{3}$

Multiply both sides of the equation by $- 4$ .

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

Simplify both sides of the equation.

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Simplify $- 4 \cdot (- \frac{y}{4})$ .

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Cancel the common factor of $4$ .

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Move the leading negative in $- \frac{y}{4}$ into the numerator.

$- 4 \cdot \frac{- y}{4} = - 4 \cdot \frac{1}{3}$

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

$4 \cdot - 1 \cdot \frac{- y}{4} = - 4 \cdot \frac{1}{3}$

Rewrite the expression.

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

Multiply.

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Multiply $- 1$ by $- 1$ .

$1 \cdot y = - 4 \cdot \frac{1}{3}$

Multiply $y$ by $1$ .

$y = - 4 \cdot \frac{1}{3}$

Simplify $- 4 \cdot \frac{1}{3}$ .

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Combine $- 4$ and $\frac{1}{3}$ .

$y = \frac{- 4}{3}$

Move the negative in front of the fraction.

$y = - \frac{4}{3}$

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{4}{3}$

Decimal Form:

$y = - 1.\overline{3}$

Mixed Number Form:

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

Solve for y 1/12+3/8y=5/12+5/8y

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