Solve for y 3(3y-1)-3(2y)=2

$3 (3 y - 1) - 3 (2 y) = 2$

Step 1

Simplify $3 (3 y - 1) - 3 \cdot (2 y)$ .

Simplify each term.

Apply the distributive property.

$3 (3 y) + 3 \cdot - 1 - 3 \cdot (2 y) = 2$

Multiply $3$ by $3$ .

$9 y + 3 \cdot - 1 - 3 \cdot (2 y) = 2$

Multiply $3$ by $- 1$ .

$9 y - 3 - 3 \cdot (2 y) = 2$

Multiply $2$ by $- 3$ .

$9 y - 3 - 6 y = 2$

Subtract $6 y$ from $9 y$ .

$3 y - 3 = 2$

Step 2

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

Add $3$ to both sides of the equation.

$3 y = 2 + 3$

Add $2$ and $3$ .

$3 y = 5$

Step 3

Divide each term in $3 y = 5$ by $3$ and simplify.

Divide each term in $3 y = 5$ by $3$ .

$\frac{3 y}{3} = \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{5}{3}$

Divide $y$ by $1$ .

$y = \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{3}$

Decimal Form:

$y = 1.\overline{6}$

Mixed Number Form:

$y = 1 \frac{2}{3}$