1) Expand the left side of the inequality:
2(y-2) = 2y - 4

Now our inequality becomes:
2y - 4 ≥ 3y + 1

Subtract 2y from both sides:
-4 ≥ y + 1

Subtract 1 from both sides:
-5 ≥ y

So the solution to the first inequality is y ≤ -5.

2) Expand the left side of the inequality:
5(y+1) = 5y + 5

Now our inequality becomes:
5y + 5 ≤ 4y + 3

Subtract 4y from both sides:
y + 5 ≤ 3

Subtract 5 from both sides:
y ≤ -2

So the solution to the second inequality is y ≤ -2.