Solve for y. -2y + 3 = -4/9y – 2/3 – 1/3y y = _____.

To solve the equation (-2y + 3 = -frac{4}{9}y – frac{2}{3} – frac{1}{3}y), let’s combine the terms on the right side.

1. Combine (-frac{4}{9}y) and (-frac{1}{3}y):

– Convert (-frac{1}{3}y) to a fraction with a denominator of 9: (-frac{1}{3}y = -frac{3}{9}y).

– Therefore, (-frac{4}{9}y – frac{3}{9}y = -frac{7}{9}y).

Now our equation becomes:

[

-2y + 3 = -frac{7}{9}y – frac{2}{3}

]

2. Next, we need to eliminate the fractions. To do this efficiently, multiply each term by 9 (the common denominator):

[

9(-2y) + 9(3) = 9left(-frac{7}{9}y – frac{2}{3}right)

]

This simplifies to:

[

-18y + 27 = -7y – 6

]

3. Now, add (18y) to both sides to get all (y)