Final answer:
The given equation, after simplification, results in 0 = 6x, indicating that both sides are equivalent. However, this expression is not among the provided options. The correct equivalent expression is 0 = 6x, showcasing the cancellation of terms on both sides during the simplification process.
Step-by-step explanation:
To determine which of the provided expressions is equivalent to -2x + 5 + 2x - 5 = -1 + (-1) + 6x + 2, we need to simplify both sides of the given equation. Let's start with the left-hand side: -2x + 2x cancels out because they are opposite terms. Similarly, +5 - 5 also cancels out. The left-hand side simplifies to 0. Now, let's simplify the right-hand side: -1 + (-1) equals -2. Add -2 + 2, which simplifies to 0. So we are left with 6x. Putting it all back together, our simplified equation is 0 = 6x. Therefore, the correct answer is not listed among the provided options. The equivalent expression to the given equation should be 0 = 6x.