Solve for y 1/3=-3/5y+3/4y-1/2y

$\frac{1}{3} = - \frac{3}{5} y + \frac{3}{4} y - \frac{1}{2} y$

Step 1

Rewrite the equation as $- \frac{3}{5} y + \frac{3}{4} y - \frac{1}{2} y = \frac{1}{3}$ .

$- \frac{3}{5} y + \frac{3}{4} y - \frac{1}{2} y = \frac{1}{3}$

Step 2

Simplify $- \frac{3}{5} y + \frac{3}{4} y - \frac{1}{2} y$ .

Simplify each term.

Combine $y$ and $\frac{3}{5}$ .

$- \frac{y \cdot 3}{5} + \frac{3}{4} y - \frac{1}{2} y = \frac{1}{3}$

Move $3$ to the left of $y$ .

$- \frac{3 \cdot y}{5} + \frac{3}{4} y - \frac{1}{2} y = \frac{1}{3}$

Combine $\frac{3}{4}$ and $y$ .

$- \frac{3 y}{5} + \frac{3 y}{4} - \frac{1}{2} y = \frac{1}{3}$

Combine $y$ and $\frac{1}{2}$ .

$- \frac{3 y}{5} + \frac{3 y}{4} - \frac{y}{2} = \frac{1}{3}$

Find the common denominator.

Multiply $\frac{3 y}{5}$ by $\frac{4}{4}$ .

$- (\frac{3 y}{5} \cdot \frac{4}{4}) + \frac{3 y}{4} - \frac{y}{2} = \frac{1}{3}$

Multiply $\frac{3 y}{5}$ by $\frac{4}{4}$ .

$- \frac{3 y \cdot 4}{5 \cdot 4} + \frac{3 y}{4} - \frac{y}{2} = \frac{1}{3}$

Multiply $\frac{3 y}{4}$ by $\frac{5}{5}$ .

$- \frac{3 y \cdot 4}{5 \cdot 4} + \frac{3 y}{4} \cdot \frac{5}{5} - \frac{y}{2} = \frac{1}{3}$

Multiply $\frac{3 y}{4}$ by $\frac{5}{5}$ .

$- \frac{3 y \cdot 4}{5 \cdot 4} + \frac{3 y \cdot 5}{4 \cdot 5} - \frac{y}{2} = \frac{1}{3}$

Multiply $\frac{y}{2}$ by $\frac{10}{10}$ .

$- \frac{3 y \cdot 4}{5 \cdot 4} + \frac{3 y \cdot 5}{4 \cdot 5} - (\frac{y}{2} \cdot \frac{10}{10}) = \frac{1}{3}$

Multiply $\frac{y}{2}$ by $\frac{10}{10}$ .

$- \frac{3 y \cdot 4}{5 \cdot 4} + \frac{3 y \cdot 5}{4 \cdot 5} - \frac{y \cdot 10}{2 \cdot 10} = \frac{1}{3}$

Reorder the factors of $5 \cdot 4$ .

$- \frac{3 y \cdot 4}{4 \cdot 5} + \frac{3 y \cdot 5}{4 \cdot 5} - \frac{y \cdot 10}{2 \cdot 10} = \frac{1}{3}$

Multiply $4$ by $5$ .

$- \frac{3 y \cdot 4}{20} + \frac{3 y \cdot 5}{4 \cdot 5} - \frac{y \cdot 10}{2 \cdot 10} = \frac{1}{3}$

Multiply $4$ by $5$ .

$- \frac{3 y \cdot 4}{20} + \frac{3 y \cdot 5}{20} - \frac{y \cdot 10}{2 \cdot 10} = \frac{1}{3}$

Multiply $2$ by $10$ .

$- \frac{3 y \cdot 4}{20} + \frac{3 y \cdot 5}{20} - \frac{y \cdot 10}{20} = \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{- 3 y \cdot 4 + 3 y \cdot 5 - y \cdot 10}{20} = \frac{1}{3}$

Simplify each term.

Multiply $4$ by $- 3$ .

$\frac{- 12 y + 3 y \cdot 5 - y \cdot 10}{20} = \frac{1}{3}$

Multiply $5$ by $3$ .

$\frac{- 12 y + 15 y - y \cdot 10}{20} = \frac{1}{3}$

Multiply $10$ by $- 1$ .

$\frac{- 12 y + 15 y - 10 y}{20} = \frac{1}{3}$

Simplify by adding terms.

Add $- 12 y$ and $15 y$ .

$\frac{3 y - 10 y}{20} = \frac{1}{3}$

Subtract $10 y$ from $3 y$ .

$\frac{- 7 y}{20} = \frac{1}{3}$

Move the negative in front of the fraction.

$- \frac{7 y}{20} = \frac{1}{3}$

Step 3

Multiply both sides of the equation by $- \frac{20}{7}$ .

$- \frac{20}{7} (- \frac{7 y}{20}) = - \frac{20}{7} \cdot \frac{1}{3}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{20}{7} (- \frac{7 y}{20})$ .

Cancel the common factor of $20$ .

Move the leading negative in $- \frac{20}{7}$ into the numerator.

$\frac{- 20}{7} (- \frac{7 y}{20}) = - \frac{20}{7} \cdot \frac{1}{3}$

Move the leading negative in $- \frac{7 y}{20}$ into the numerator.

$\frac{- 20}{7} \cdot \frac{- 7 y}{20} = - \frac{20}{7} \cdot \frac{1}{3}$

Factor $20$ out of $- 20$ .

$\frac{20 (- 1)}{7} \cdot \frac{- 7 y}{20} = - \frac{20}{7} \cdot \frac{1}{3}$

Cancel the common factor.

$\frac{20 \cdot - 1}{7} \cdot \frac{- 7 y}{20} = - \frac{20}{7} \cdot \frac{1}{3}$

Rewrite the expression.

$\frac{- 1}{7} (- 7 y) = - \frac{20}{7} \cdot \frac{1}{3}$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 y$ .

$\frac{- 1}{7} (7 (- y)) = - \frac{20}{7} \cdot \frac{1}{3}$

Cancel the common factor.

$\frac{- 1}{7} (7 (- y)) = - \frac{20}{7} \cdot \frac{1}{3}$

Rewrite the expression.

$- - y = - \frac{20}{7} \cdot \frac{1}{3}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{20}{7} \cdot \frac{1}{3}$

Multiply $y$ by $1$ .

$y = - \frac{20}{7} \cdot \frac{1}{3}$

Simplify the right side.

Multiply $- \frac{20}{7} \cdot \frac{1}{3}$ .

Multiply $\frac{1}{3}$ by $\frac{20}{7}$ .

$y = - \frac{20}{3 \cdot 7}$

Multiply $3$ by $7$ .

$y = - \frac{20}{21}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{20}{21}$

Decimal Form:

$y = - 0.\overline{952380}$

Solve for y 1/3=-3/5y+3/4y-1/2y

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