Let's solve the equation step by step.

Given equation:
\[
3[x - 2(x - 1) - 3(x + 2)] = -(x - 4) - 5
\]

### Step 1: Expand the terms inside the brackets.
\[
3[x - 2(x - 1) - 3(x + 2)]
\]

Start with \( 2(x - 1) \) and \( 3(x + 2) \):
\[
2(x - 1) = 2x - 2
\]
\[
3(x + 2) = 3x + 6
\]

Substitute these into the equation:
\[
3[x - (2x - 2) - (3x + 6)] = -(x - 4) - 5
\]

### Step 2: Simplify inside the brackets.
\[
x - (2x - 2) - (3x + 6)
\]
Distribute the negative signs:
\[
x - 2x + 2 - 3x - 6 = -4x - 4
\]

So, the equation becomes:
\[
3(-4x - 4) = -(x - 4) - 5
\]

### Step 3: Multiply the 3 on the left side.
\[
-12x - 12 = -(x - 4) - 5
\]

### Step 4: Simplify the right side.
\[
-(x - 4) = -x + 4
\]
So the equation becomes:
\[
-12x - 12 = -x + 4 - 5
\]
\[
-12x - 12 = -x - 1
\]

### Step 5: Bring all \(x\)-terms to one side and constant terms to the other side.
\[
-12x + x = -1 + 12
\]
\[
-11x = 11
\]

### Step 6: Solve for \(x\).
\[
x = \frac{11}{-11} = -1
\]

So, the solution is \( x = -1 \).

---

Would you like further details or have any questions about the process?

Here are 5 questions to deepen your understanding:
1. How do you simplify expressions with parentheses and distribute terms?
2. What happens when you distribute negative signs through parentheses?
3. Why do we move variables to one side and constants to the other?
4. How do you verify the solution by plugging \( x = -1 \) back into the original equation?
5. What role does the equality sign play in maintaining balance between the two sides?

**Tip:** Always simplify the equation step by step to avoid errors during expansion or distribution.

Learn how to solve the equation 3[x-2(x-1)-3(x+2)]=-(x-4)-5 with a detailed step-by-step solution. This problem involves algebraic concepts such as distribution and simplification of expressions. Suitable for high school students in Grades 9-12.

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