Solve for y -1/3y+10=-2/3y+7

$- \frac{1}{3} y + 10 = - \frac{2}{3} y + 7$

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

$- \frac{y}{3} + 10 = - \frac{2}{3} y + 7$

Simplify each term.

Combine $y$ and $\frac{2}{3}$ .

$- \frac{y}{3} + 10 = - \frac{y \cdot 2}{3} + 7$

Move $2$ to the left of $y$ .

$- \frac{y}{3} + 10 = - \frac{2 y}{3} + 7$

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

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

$- \frac{y}{3} + 10 + \frac{2 y}{3} = 7$

Combine the numerators over the common denominator.

$10 + \frac{- y + 2 y}{3} = 7$

Add $- y$ and $2 y$ .

$10 + \frac{y}{3} = 7$

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

Subtract $10$ from both sides of the equation.

$\frac{y}{3} = 7 - 10$

Subtract $10$ from $7$ .

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

Multiply both sides of the equation by $3$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 3 \cdot - 3$

Simplify the right side.

Multiply $3$ by $- 3$ .

$y = - 9$