Simplify the following algebraic expressions and solve the inequalities.

here are the solutions to the problems.

1. Simplify $7a + 12a - 12$

Step 1: Combine like terms.

$$7a + 12a - 12 = (7+12)a - 12$$ $$= 19a - 12$$

The simplified expression is $\boxed{19a - 12}$.

2. Simplify $2x - 3(3 - 2(y - 4x))$

Step 1: Distribute the $-2$ inside the innermost parenthesis.

$$2x - 3(3 - 2(y - 4x)) = 2x - 3(3 - 2y + 8x)$$

Step 2: Distribute the $-3$ to the terms inside the parenthesis.

$$= 2x - 9 + 6y - 24x$$

Step 3: Combine like terms.

$$= (2x - 24x) + 6y - 9$$ $$= -22x + 6y - 9$$

Rearranging the terms:

$$= 6y - 22x - 9$$

The simplified expression is $\boxed{6y - 22x - 9}$.

3. Solve the inequalities