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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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 the numerators over the common denominator.

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

Subtract $5 y$ from $3 y$ .

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

Simplify each term.

Cancel the common factor of $- 2$ and $8$ .

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

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

Cancel the common factors.

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.

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

Step 4

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

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 $12$ .

Factor $4$ out of $4$ .

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

Cancel the common factors.

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.

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

Step 5

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

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $y$ by $1$ .

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

Simplify the right side.

Simplify $- 4 (\frac{1}{3})$ .

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

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

Move the negative in front of the fraction.

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

Step 7

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

Related Questions

Support LCMGCF.com by disabling your adblocker.