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To solve the equation \(3 - (x - 1) = -1 - (5 - x)\), let's go through the steps in detail.

### Step 1: Simplify Each Side
First, distribute the minus signs within the parentheses on both sides.

\[
3 - x + 1 = -1 - 5 + x
\]

### Step 2: Combine Like Terms
Now, combine the constants and \(x\)-terms on each side:

\[
(3 + 1) - x = (-1 - 5) + x
\]
\[
4 - x = -6 + x
\]

### Step 3: Move \(x\)-Terms to One Side
To eliminate \(x\) from one side, add \(x\) to both sides:

\[
4 = -6 + 2x
\]

### Step 4: Solve for \(x\)
Now, isolate \(x\) by adding 6 to both sides:

\[
10 = 2x
\]

Finally, divide by 2:

\[
x = 5
\]

### Step 5: Check the Solution
Substitute \(x = 5\) back into the original equation to verify:

\[
3 - (5 - 1) = -1 - (5 - 5)
\]
\[
3 - 4 = -1 - 0
\]
\[
-1 = -1
\]

The left side equals the right side, so \(x = 5\) is indeed the solution.

---

Would you like more details on any specific step, or do you have any questions?

### Related Questions
1. How do you handle equations with variables on both sides?
2. What are some tips for checking solutions in equations?
3. How does distributing negative signs work in equations?
4. What should you do if there are fractions in the equation?
5. Can this method be used for inequalities as well?

### Tip
Always simplify each side of the equation first, as this can often make the solution process much easier.

Solve the following equation: 3 - (x - 1) = -1 - (5 - x)

Learn how to solve the linear equation 3 - (x - 1) = -1 - (5 - x) with a step-by-step approach. This problem covers algebraic concepts, including simplifying expressions and isolating variables. Ideal for students in Grades 7-9.

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