Solve for y 3(y+2)+2y=7(y-1)+9

$3 (y + 2) + 2 y = 7 (y - 1) + 9$

Step 1

Simplify $3 (y + 2) + 2 y$ .

Simplify each term.

Apply the distributive property.

$3 y + 3 \cdot 2 + 2 y = 7 (y - 1) + 9$

Multiply $3$ by $2$ .

$3 y + 6 + 2 y = 7 (y - 1) + 9$

Add $3 y$ and $2 y$ .

$5 y + 6 = 7 (y - 1) + 9$

Step 2

Simplify $7 (y - 1) + 9$ .

Simplify each term.

Apply the distributive property.

$5 y + 6 = 7 y + 7 \cdot - 1 + 9$

Multiply $7$ by $- 1$ .

$5 y + 6 = 7 y - 7 + 9$

Add $- 7$ and $9$ .

$5 y + 6 = 7 y + 2$

Step 3

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

Subtract $7 y$ from both sides of the equation.

$5 y + 6 - 7 y = 2$

Subtract $7 y$ from $5 y$ .

$- 2 y + 6 = 2$

Step 4

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

Subtract $6$ from both sides of the equation.

$- 2 y = 2 - 6$

Subtract $6$ from $2$ .

$- 2 y = - 4$

Step 5

Divide each term in $- 2 y = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 4$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 4}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$y = 2$