Solve for y -2y+3=-4/9y-2/3-1/3y

$- 2 y + 3 = - \frac{4}{9} y - \frac{2}{3} - \frac{1}{3} y$

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- \frac{4}{9} y - \frac{2}{3} - \frac{1}{3} y = - 2 y + 3$

Simplify $- \frac{4}{9} y - \frac{2}{3} - \frac{1}{3} y$ .

Simplify each term.

Combine $y$ and $\frac{4}{9}$ .

$- \frac{y \cdot 4}{9} - \frac{2}{3} - \frac{1}{3} y = - 2 y + 3$

Move $4$ to the left of $y$ .

$- \frac{4 \cdot y}{9} - \frac{2}{3} - \frac{1}{3} y = - 2 y + 3$

Combine $y$ and $\frac{1}{3}$ .

$- \frac{4 y}{9} - \frac{2}{3} - \frac{y}{3} = - 2 y + 3$

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

$- \frac{4 y}{9} - \frac{y}{3} \cdot \frac{3}{3} - \frac{2}{3} = - 2 y + 3$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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

$- \frac{4 y}{9} - \frac{y \cdot 3}{3 \cdot 3} - \frac{2}{3} = - 2 y + 3$

Multiply $3$ by $3$ .

$- \frac{4 y}{9} - \frac{y \cdot 3}{9} - \frac{2}{3} = - 2 y + 3$

Combine the numerators over the common denominator.

$\frac{- 4 y - y \cdot 3}{9} - \frac{2}{3} = - 2 y + 3$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $- 4 y - y \cdot 3$ .

Factor $y$ out of $- 4 y$ .

$\frac{y \cdot - 4 - y \cdot 3}{9} - \frac{2}{3} = - 2 y + 3$

Factor $y$ out of $- y \cdot 3$ .

$\frac{y \cdot - 4 + y (- 1 \cdot 3)}{9} - \frac{2}{3} = - 2 y + 3$

Factor $y$ out of $y \cdot - 4 + y (- 1 \cdot 3)$ .

$\frac{y (- 4 - 1 \cdot 3)}{9} - \frac{2}{3} = - 2 y + 3$

Multiply $- 1$ by $3$ .

$\frac{y (- 4 - 3)}{9} - \frac{2}{3} = - 2 y + 3$

Subtract $3$ from $- 4$ .

$\frac{y \cdot - 7}{9} - \frac{2}{3} = - 2 y + 3$

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

$\frac{- 7 \cdot y}{9} - \frac{2}{3} = - 2 y + 3$

Move the negative in front of the fraction.

$- \frac{7 y}{9} - \frac{2}{3} = - 2 y + 3$

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

Add $2 y$ to both sides of the equation.

$- \frac{7 y}{9} - \frac{2}{3} + 2 y = 3$

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{7 y}{9} + 2 y \cdot \frac{9}{9} - \frac{2}{3} = 3$

Combine $2 y$ and $\frac{9}{9}$ .

$- \frac{7 y}{9} + \frac{2 y \cdot 9}{9} - \frac{2}{3} = 3$

Combine the numerators over the common denominator.

$\frac{- 7 y + 2 y \cdot 9}{9} - \frac{2}{3} = 3$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $- 7 y + 2 y \cdot 9$ .

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

$\frac{y \cdot - 7 + 2 y \cdot 9}{9} - \frac{2}{3} = 3$

Factor $y$ out of $2 y \cdot 9$ .

$\frac{y \cdot - 7 + y (2 \cdot 9)}{9} - \frac{2}{3} = 3$

Factor $y$ out of $y \cdot - 7 + y (2 \cdot 9)$ .

$\frac{y (- 7 + 2 \cdot 9)}{9} - \frac{2}{3} = 3$

Multiply $2$ by $9$ .

$\frac{y (- 7 + 18)}{9} - \frac{2}{3} = 3$

Add $- 7$ and $18$ .

$\frac{y \cdot 11}{9} - \frac{2}{3} = 3$

Move $11$ to the left of $y$ .

$\frac{11 y}{9} - \frac{2}{3} = 3$

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

Add $\frac{2}{3}$ to both sides of the equation.

$\frac{11 y}{9} = 3 + \frac{2}{3}$

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

$\frac{11 y}{9} = 3 \cdot \frac{3}{3} + \frac{2}{3}$

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

$\frac{11 y}{9} = \frac{3 \cdot 3}{3} + \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{11 y}{9} = \frac{3 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{11 y}{9} = \frac{9 + 2}{3}$

Add $9$ and $2$ .

$\frac{11 y}{9} = \frac{11}{3}$

Multiply both sides of the equation by $\frac{9}{11}$ .

$\frac{9}{11} \cdot \frac{11 y}{9} = \frac{9}{11} \cdot \frac{11}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{9}{11} \cdot \frac{11 y}{9}$ .

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9}{11} \cdot \frac{11 y}{9} = \frac{9}{11} \cdot \frac{11}{3}$

Rewrite the expression.

$\frac{1}{11} (11 y) = \frac{9}{11} \cdot \frac{11}{3}$

Cancel the common factor of $11$ .

Factor $11$ out of $11 y$ .

$\frac{1}{11} (11 (y)) = \frac{9}{11} \cdot \frac{11}{3}$

Cancel the common factor.

$\frac{1}{11} (11 y) = \frac{9}{11} \cdot \frac{11}{3}$

Rewrite the expression.

$y = \frac{9}{11} \cdot \frac{11}{3}$

Simplify the right side.

Simplify $\frac{9}{11} \cdot \frac{11}{3}$ .

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$y = \frac{3 (3)}{11} \cdot \frac{11}{3}$

Cancel the common factor.

$y = \frac{3 \cdot 3}{11} \cdot \frac{11}{3}$

Rewrite the expression.

$y = \frac{3}{11} \cdot 11$

Cancel the common factor of $11$ .

Cancel the common factor.

$y = \frac{3}{11} \cdot 11$

Rewrite the expression.

$y = 3$

Solve for y -2y+3=-4/9y-2/3-1/3y

Related Questions

Support LCMGCF.com by disabling your adblocker.