To solve this equation, we need to combine like terms on the left side:

1 1/2у + 3 2/5у = 1 1/3у - 2 7/15у + 2 1/2

Let's convert the mixed numbers to improper fractions:

3/2у + 17/5у = 4/3у - 37/15у + 5/2

Now, we can add and subtract the terms:

(3/2 + 17/5)у = (4/3 - 37/15)у + 5/2
(15/10 + 34/10)у = (20/15 - 37/15)у + 5/2
49/10у = - 17/15у + 5/2

Now, let's get rid of the fractions by multiplying all terms by the least common multiple of the denominators, which is 30:

30(49/10у) = 30(-17/15у) + 30(5/2)
147y = -34y + 75

Now, solve for y:

147y + 34y = 75
181y = 75
y = 75/181

So, y = 75/181.