Final answer:
The equation -5x+12=-5x-12 does not have exactly one solution.
Step-by-step explanation:
To determine if the equation -5x+12=-5x-12 has exactly one solution, we can simplify it:
-5x + 12 = -5x - 12
Adding 5x to both sides gives: 12 = -12
Since the equation is contradictory (12 cannot equal -12), there is no solution for x. So, the equation does not have exactly one solution.