Solve for y 5y-(2(y+1)+2)=7y

$5 y - (2 (y + 1) + 2) = 7 y$

Simplify $5 y - (2 (y + 1) + 2)$ .

Simplify each term.

Apply the distributive property.

$5 y - (2 y + 2 \cdot 1 + 2) = 7 y$

Multiply $2$ by $1$ .

$5 y - (2 y + 2 + 2) = 7 y$

Add $2$ and $2$ .

$5 y - (2 y + 4) = 7 y$

Apply the distributive property.

$5 y - (2 y) - 1 \cdot 4 = 7 y$

Multiply $2$ by $- 1$ .

$5 y - 2 y - 1 \cdot 4 = 7 y$

Multiply $- 1$ by $4$ .

$5 y - 2 y - 4 = 7 y$

Subtract $2 y$ from $5 y$ .

$3 y - 4 = 7 y$

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

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

$3 y - 4 - 7 y = 0$

Subtract $7 y$ from $3 y$ .

$- 4 y - 4 = 0$

Add $4$ to both sides of the equation.

$- 4 y = 4$

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $4$ by $- 4$ .

$y = - 1$