To solve the equation:

$3 - (x - 1) = -1 - (5 - x)$

we'll go through the steps carefully.

Step 1: Distribute and Simplify

First, distribute the negative signs on both sides.

On the left side: $3 - (x - 1) = 3 - x + 1 = 4 - x$

On the right side: $-1 - (5 - x) = -1 - 5 + x = -6 + x$

So, we now have: $4 - x = -6 + x$

Step 2: Move $x$ Terms to One Side

Add $x$ to both sides to eliminate $-x$ on the left: $4 = -6 + 2x$

Step 3: Isolate $x$

Add 6 to both sides to isolate terms with $x$: $10 = 2x$

Then, divide by 2: $x = 5$

Step 4: Check the Solution

Substitute $x = 5$ back into the original equation to verify:

$3 - (5 - 1) = -1 - (5 - 5)$

Simplify both sides:

• Left side: $3 - 4 = -1$
• Right side: $-1 - 0 = -1$

Both sides are equal, so the solution is correct.

Final Answer:

$x = 5$

Would you like further details on any step?

Here are five related questions:

1. How would the solution change if the signs in the parentheses were different?
2. What steps would you take if there were fractions involved?
3. Can this equation be solved graphically? If so, how?
4. How would you solve an equation with absolute values instead of parentheses?
5. What are common mistakes to avoid in similar problems?

Tip: Always re-check your result by substituting the value back into the original equation. This ensures accuracy.