`2x-[3y-{2x-(y-x)}]=?`

Options

A. `5x-4y`
B. `4y-5x`
C. `5y-4x`
D. `4x-5y`

Answer

To solve the expression \( 2x - [3y - \{2x - (y - x)\}] \), we will follow the order of operations, which dictates that we should solve the innermost brackets first and work our way outwards.

### Step-by-Step Solution:

1. **Start with the innermost bracket**:
\[ (y - x) \]
This expression remains as it is for now.

**Hint**: Identify the innermost bracket to simplify first.

2. **Substitute the innermost bracket into the curly bracket**:
\[ 2x - (y - x) = 2x - y + x = 3x - y \]
Now, replace \(2x - (y - x)\) with \(3x - y\).

**Hint**: Remember to change the signs when distributing the negative.

3. **Now substitute back into the curly bracket**:
\[ 3y - \{3x - y\} \]
This becomes:
\[ 3y - 3x + y = 4y - 3x \]

**Hint**: When you distribute the negative sign, ensure all terms inside the curly bracket change appropriately.

4. **Now substitute this back into the square bracket**:
\[ 2x - [4y - 3x] \]
This simplifies to:
\[ 2x - 4y + 3x = 5x - 4y \]

**Hint**: Again, remember to change the signs when distributing the negative sign.

5. **Final expression**:
The final simplified expression is:
\[ 5x - 4y \]

### Final Answer:
\[ 5x - 4y \]