To determine which of the given equations has a solution of -12, we need to substitute -12 for the variable in each equation and verify if the result is true.
Let's go through each equation one by one:
1. x + 12 = -1: If we substitute -12 for x, we get -12 + 12 = -1, which simplifies to 0 = -1. This is not true, so this equation does not have -12 as a solution.
2. x + (1/2) = -1: Substituting -12 for x gives -12 + (1/2) = -1. Simplifying this equation, we get -23/2 = -1, which is not true. Therefore, this equation does not have -12 as a solution.
3. x - 1 = -12: By substituting -12 for x, we have -12 - 1 = -12, which simplifies to -13 = -12. This equation is also not true, so it does not have -12 as a solution.
4. x + 1 = 12: Substituting -12 for x gives -12 + 1 = 12. Simplifying this equation, we get -11 = 12, which is once again not true. Therefore, this equation does not have -12 as a solution.
5. x - 12 = 1: By substituting -12 for x, we have -12 - 12 = 1, which simplifies to -24 = 1. This equation is not true either, so it does not have -12 as a solution.
Based on the above analysis, none of the given equations has a solution of -12.