To solve this inequality, we need to first distribute the -1 to both terms inside the parentheses:

12 - (x + 2) > 12x - 11
12 - x - 2 > 12x - 11
10 - x > 12x - 11

Next, we need to simplify the equation by combining like terms:

10 - x > 12x - 11
10 + 11 > 12x - x
21 > 11x

Now, we divide both sides by 11 to solve for x:

21/11 > x
1.909 > x

Therefore, the solution to the inequality 12 - (x + 2) > 12x - 11 is x < 1.909.