1) 7 - 3x = 4x + 3

First, let's combine like terms by moving the variables to one side of the equation and the constants to the other side:

7 - 3 = 4x + 3 + 3
4 = 4x + 6

Next, let's isolate the variable by subtracting 6 from both sides:

4 - 6 = 4x
-2 = 4x

Finally, divide by 4 to solve for x:

-2/4 = x
x = -1/2

Therefore, the solution is x = -1/2.

2) -3(2y + 7) - 1 = 12

First, distribute the -3 to both terms inside the parentheses:

-6y - 21 - 1 = 12

Combine like terms:

-6y - 22 = 12

Next, add 22 to both sides to isolate the variable:

-6y = 34

Lastly, divide by -6 to solve for y:

y = -34/6
y = -17/3

Therefore, the solution is y = -17/3.