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stonecold
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stonecold
If \(|\frac{y}{2}- \frac{1}{6}| < \frac{2}{3}\), then y could be all of the following EXCEPT

A. \(-\frac{4}{3}\)

B. \(-\frac{5}{6}\)

C. 0

D. \(\frac{5}{6}\)

E. \(\frac{4}{3}\)

For this absolute value problem, we have two cases to consider: when (y/2 - ⅙) is positive and when (y/2 - ⅙) is negative. Let’s start with the positive case:

Case 1: (y/2 - ⅙) is positive

y/2 - 1/6 < 2/3

Multiplying by 6, we have:

3y - 1 < 4

3y < 5

y < 5/3

Case 2: (y/2 - ⅙) is negative

-(y/2 - ⅙) < 2/3

-y/2 + 1/6 < ⅔

Multiplying by 6, we have:

-3y + 1 < 4

-3y < 3

y > -1

Thus, -1 < y < 5/3. Thus, y cannot be -4/3.

Answer: A
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