Final answer:
The equations c) 2x - 4 = 2x + 4 and d) x + 5 = x - 5 have no solutions, as solving both results in contradictory statements, while a) and b) have an infinite number of solutions.
Step-by-step explanation:
The equation that has no solutions is option c) 2x - 4 = 2x + 4. To determine if there are no solutions, we can attempt to solve the equation by subtracting 2x from both sides. We are left with -4 = 4, which is an impossible statement, indicating that there are no solutions. In contrast, options a) and b) are examples of identities, where both sides of the equation are always equal regardless of the value of x. This means that they have an infinite number of solutions. Option d), on the other hand, gives a contradictory statement when solved: if we subtract x from both sides, we get 5 = -5, which also indicates no solutions because it's impossible.