Solve for y -2+y=2(1/3y-3)

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

Step 1

Simplify $2 (\frac{1}{3} y - 3)$ .

Rewrite.

$- 2 + y = 0 + 0 + 2 (\frac{1}{3} y - 3)$

Simplify by adding zeros.

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

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

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

Apply the distributive property.

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

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

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

Multiply $2$ by $- 3$ .

$- 2 + y = \frac{2 y}{3} - 6$

Step 2

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

Subtract $\frac{2 y}{3}$ from both sides of the equation.

$- 2 + y - \frac{2 y}{3} = - 6$

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

$- 2 + y \cdot \frac{3}{3} - \frac{2 y}{3} = - 6$

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

$- 2 + \frac{y \cdot 3}{3} - \frac{2 y}{3} = - 6$

Combine the numerators over the common denominator.

$- 2 + \frac{y \cdot 3 - 2 y}{3} = - 6$

Subtract $2 y$ from $y \cdot 3$ .

Reorder $y$ and $3$ .

$- 2 + \frac{3 \cdot y - 2 y}{3} = - 6$

Subtract $2 y$ from $3 \cdot y$ .

$- 2 + \frac{y}{3} = - 6$

Step 3

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

Add $2$ to both sides of the equation.

$\frac{y}{3} = - 6 + 2$

Add $- 6$ and $2$ .

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

Step 4

Multiply both sides of the equation by $3$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 3 \cdot - 4$

Simplify the right side.

Multiply $3$ by $- 4$ .

$y = - 12$

Solve for y -2+y=2(1/3y-3)

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