Final answer:
The equation 2(x + 6) = 2x - 10 simplifies to 12 = -10 after canceling out the x terms, which is not possible, indicating no solutions exist for this equation.
Step-by-step explanation:
The question asks how many solutions the equation 2(x + 6) = 2x - 10 has.
To find the solution, we should first simplify and solve the equation. Distributing the 2 on the left side, we get 2x + 12 = 2x - 10. We then attempt to isolate x by subtracting 2x from both sides, but we end up with 12 = -10, which is not possible.
Therefore, since the variables cancel each other out and we are left with a false statement, this indicates that there are no solutions to the equation, as it is inconsistent.