Solve for y 5(y+1)+2=4(y+2)-6

$5 (y + 1) + 2 = 4 (y + 2) - 6$

Step 1

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

Simplify each term.

Apply the distributive property.

$5 y + 5 \cdot 1 + 2 = 4 (y + 2) - 6$

Multiply $5$ by $1$ .

$5 y + 5 + 2 = 4 (y + 2) - 6$

Add $5$ and $2$ .

$5 y + 7 = 4 (y + 2) - 6$

Step 2

Simplify $4 (y + 2) - 6$ .

Simplify each term.

Apply the distributive property.

$5 y + 7 = 4 y + 4 \cdot 2 - 6$

Multiply $4$ by $2$ .

$5 y + 7 = 4 y + 8 - 6$

Subtract $6$ from $8$ .

$5 y + 7 = 4 y + 2$

Step 3

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

Subtract $4 y$ from both sides of the equation.

$5 y + 7 - 4 y = 2$

Subtract $4 y$ from $5 y$ .

$y + 7 = 2$

Step 4

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

Subtract $7$ from both sides of the equation.

$y = 2 - 7$

Subtract $7$ from $2$ .

$y = - 5$