Solve for y 3(3-y)+1=31

$3 (3 - y) + 1 = 31$

Step 1

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

Simplify each term.

Apply the distributive property.

$3 \cdot 3 + 3 (- y) + 1 = 31$

Multiply $3$ by $3$ .

$9 + 3 (- y) + 1 = 31$

Multiply $- 1$ by $3$ .

$9 - 3 y + 1 = 31$

Add $9$ and $1$ .

$- 3 y + 10 = 31$

Step 2

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

Subtract $10$ from both sides of the equation.

$- 3 y = 31 - 10$

Subtract $10$ from $31$ .

$- 3 y = 21$

Step 3

Divide each term in $- 3 y = 21$ by $- 3$ and simplify.

Divide each term in $- 3 y = 21$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{21}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{21}{- 3}$

Divide $y$ by $1$ .

$y = \frac{21}{- 3}$

Simplify the right side.

Divide $21$ by $- 3$ .

$y = - 7$