Simplify :
`3x - [4x - bar(3x -5y) - 3{2x - (3x - bar(2x - 3y))}]`

Answer

To simplify the expression \( 3x - [4x - \overline{(3x - 5y)} - 3\{2x - (3x - \overline{(2x - 3y)})\}] \), we will follow the order of operations and carefully handle the brackets and bars.

### Step-by-step Solution:

1. **Start with the innermost expression:**
\[ 3x - \overline{(2x - 3y)} \]
The bar indicates that we need to negate the expression inside:
\[ \overline{(2x - 3y)} = -2x + 3y \]
Therefore,
\[ 3x - \overline{(2x - 3y)} = 3x + 2x - 3y = 5x - 3y \]

2. **Substituting back into the expression:**
Now we replace \( \overline{(2x - 3y)} \) in the original expression:
\[ 3x - [4x - \overline{(3x - 5y)} - 3\{2x - (5x - 3y)\}] \]

3. **Next, simplify \( \overline{(3x - 5y)} \):**
\[ \overline{(3x - 5y)} = -3x + 5y \]
Substitute this back:
\[ 3x - [4x - (-3x + 5y) - 3\{2x - (5x - 3y)\}] \]

4. **Now simplify the expression inside the brackets:**
\[ 4x - (-3x + 5y) = 4x + 3x - 5y = 7x - 5y \]

5. **Now simplify \( 2x - (5x - 3y) \):**
\[ 2x - (5x - 3y) = 2x - 5x + 3y = -3x + 3y \]

6. **Now substitute this back into the expression:**
\[ 3x - [7x - 5y - 3(-3x + 3y)] \]
Distributing the -3:
\[ 3x - [7x - 5y + 9x - 9y] \]
Combine like terms:
\[ 3x - [16x - 14y] \]

7. **Now simplify the outer expression:**
\[ 3x - 16x + 14y = -13x + 14y \]

### Final Simplified Expression:
\[ \boxed{-13x + 14y} \]