Solve the equation 1/3 (y + 7) = 3(y – 1) for y.
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Solve the equation 1/3 (y + 7) = 3(y – 1) for y.
To solve the equation (frac{1}{3}(y + 7) = 3(y – 1)), we’ll follow these steps:
1. Eliminate the fraction: Multiply both sides by 3 to get rid of the fraction.
[
y + 7 = 9(y – 1)
]
2. Distribute on the right side:
[
y + 7 = 9y – 9
]
3. Move all terms involving (y) to one side and constant terms to the other side:
[
7 + 9 = 9y – y
]
[
16 = 8y
]
4. Solve for (y):
[
y = frac{16}{8} = 2
]
So, the solution to the equation is (y = 2).
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