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