can you help me with this math problem?

Question

9 - | 2 - 1 over 3y| = 0 and can you explain to me how you do it and give me a positive and a negative answer for it? step by step thank you

Answer 1

9 - | 2 - 1/(3y) | = 0
9 = | 2 - 1/(3y) |

So now you have to create two versions:
9 = +(2 - 1/(3y)) or 9 = -(2 - 1/(3y))

Then just solve them separately.
Case 1:
9 = 2 - 1/(3y)
7 = -1/(3y)
3y = -1/7
y = -1/21

Case 2:
9 = -2 + 1/(3y)
11 = 1/(3y)
3y = 1/11
y = 1/33

So your two answers are y = -1/21 or y = 1/33