Final answer:
The equation 2(x-1)=2x-2 simplifies to 0=0, which is an identity and true for all values of x; therefore, it has an infinite number of solutions.
Step-by-step explanation:
To determine whether the equation 2(x-1)=2x-2 has one solution, no solutions, or an infinite number of solutions, we need to simplify and solve the equation. First, distribute the 2 on the left-hand side:
2x - 2 = 2x - 2
Now, subtract 2x from both sides of the equation:
2x - 2x - 2 = 2x - 2x - 2
Which simplifies to:
0 = 0
This indicates that the equation is true for all values of x. Therefore, the equation 2(x-1)=2x-2 has an infinite number of solutions since it is an identity.