Solve for y 5(y+1)-y=3(y-1)+7

$5 (y + 1) - y = 3 (y - 1) + 7$

Step 1

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

Simplify each term.

Apply the distributive property.

$5 y + 5 \cdot 1 - y = 3 (y - 1) + 7$

Multiply $5$ by $1$ .

$5 y + 5 - y = 3 (y - 1) + 7$

Subtract $y$ from $5 y$ .

$4 y + 5 = 3 (y - 1) + 7$

Step 2

Simplify $3 (y - 1) + 7$ .

Simplify each term.

Apply the distributive property.

$4 y + 5 = 3 y + 3 \cdot - 1 + 7$

Multiply $3$ by $- 1$ .

$4 y + 5 = 3 y - 3 + 7$

Add $- 3$ and $7$ .

$4 y + 5 = 3 y + 4$

Step 3

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

Subtract $3 y$ from both sides of the equation.

$4 y + 5 - 3 y = 4$

Subtract $3 y$ from $4 y$ .

$y + 5 = 4$

Step 4

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

Subtract $5$ from both sides of the equation.

$y = 4 - 5$

Subtract $5$ from $4$ .

$y = - 1$