Final answer:
The given equation 8+2(x-6)=-2+2x-2, after simplification and combining like terms, is found to be an identity. This means that it holds true for all values of x and therefore it has infinite solutions.
Step-by-step explanation:
The question is asking to find out if the given equation 8+2(x-6)=-2+2x-2 has one solution, no solutions or perhaps even multiple solutions.
Let's first simplify the equation. Start by distributing the '2' in 2(x-6) to get 2x - 12. So the equation becomes 8 + 2x -12 = -2 + 2x - 2.
Combining like terms gives us 2x - 4 = 2x - 4.
The result implies that the given equation is an identity, meaning that it is true for all values of x, and it therefore has infinite solutions.
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