Find All Complex Solutions 5(y+1)-y=4(y-1)+9

$5 (y + 1) - y = 4 (y - 1) + 9$

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

Simplify each term.

Apply the distributive property.

$5 y + 5 \cdot 1 - y = 4 (y - 1) + 9$

Multiply $5$ by $1$ .

$5 y + 5 - y = 4 (y - 1) + 9$

Subtract $y$ from $5 y$ .

$4 y + 5 = 4 (y - 1) + 9$

Simplify $4 (y - 1) + 9$ .

Simplify each term.

Apply the distributive property.

$4 y + 5 = 4 y + 4 \cdot - 1 + 9$

Multiply $4$ by $- 1$ .

$4 y + 5 = 4 y - 4 + 9$

Add $- 4$ and $9$ .

$4 y + 5 = 4 y + 5$

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

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

$4 y + 5 - 4 y = 5$

Combine the opposite terms in $4 y + 5 - 4 y$ .

Subtract $4 y$ from $4 y$ .

$0 + 5 = 5$

Add $0$ and $5$ .

$5 = 5$

Since $5 = 5$ , the equation will always be true.

Always true