Equations A and C have exactly one solution, while equations B and D have no solution.
To determine which equations have exactly one solution, we need to analyze their properties.
A. -103x - 6 = -6x - 103: This equation can be simplified by combining like terms to yield -97x - 6 = -103. By further simplifying, we find -97x = -97, and upon dividing by -97, we get x = 1. This equation has one solution, x = 1.
B. -6x - 6 = -6x - 103: Subtracting -6x from both sides, we obtain -6 = -103, which is a contradiction. This equation has no solution.
C. -6x - 6 = 103x - 103: By combining like terms, we get -6 = 109x - 103. Then, adding 103 to both sides, we have 97 = 109x. Dividing by 109 gives x ≈ 0.8899. This equation has one solution.
D. 103x - 6 = 103x - 103: Subtracting 103x from both sides, we obtain -6 = -103, which is a contradiction. This equation has no solution.
