Our task is to solve the inequality 12t - 2 < -5t + 36 for the variable t. Let's first gather like terms.
The first step in solving an inequality is to bring the terms with variables on one side and the constants on the other.
So, our inequality 12t - 2 < -5t + 36 becomes 12t + 5t < 36 + 2
by moving the -5t from the right side to the left (changing the sign as we move them to the other side of the inequality sign), and the -2 from the left side to the right (changing its sign as well).
This simplifies to 17t < 38.
The next step would be to isolate the variable t. We can achieve this by dividing all the terms in the inequality by 17, which is the coefficient of t.
Therefore, we end up with t < 38 / 17.
Now, let's check the given options. The correct answer would be the one that matches the resulting inequality for t.
Looking at these options: a) t > 3 b) t < 3 c) t ≥ 3 d) t ≤ 3, we find that none of them matches the resulting inequality for t. Therefore, none of the given options is correct.
This could imply either there is an error in the problem statement or the given options do not cover the range for the potential solution to the problem.