To solve the equation \(2x - (x - 1) = (x - 1) - (x + 1)\), let's simplify both sides step by step:

1. **Distribute the negative signs:**
   \[
   2x - x + 1 = x - 1 - x - 1
   \]

2. **Combine like terms:**
   \[
   (2x - x) + 1 = (x - x) + (-1 - 1)
   \]
   \[
   x + 1 = 0 - 2
   \]
   \[
   x + 1 = -2
   \]

3. **Solve for \(x\):**
   \[
   x = -2 - 1
   \]
   \[
   x = -3
   \]

So, the solution to the equation is \(\boxed{x = -3}\).

Would you like more details on the steps, or do you have any other questions?

Here are some related questions you might find interesting:
1. How would the solution change if the equation was \(2x - (x + 1) = (x - 1) - (x + 1)\)?
2. What is the effect of multiplying both sides of an equation by a negative number?
3. How can you verify the solution of an equation?
4. What happens if there are variables on both sides of an equation?
5. How do you solve equations involving fractions?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 2x - (x-1) = (x-1) - (x+1) step-by-step with a detailed solution. This problem involves algebraic concepts such as equations and simplification. Suitable for students in Grades 7-9.

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