Select the correct option to make the given expression true.
`45 - (-11) - (-25) + (-42) ? (-3) + 57 + (-4) - (-42)`

Options

A. `gt`
B. `lt`
C. =
D. Can't determined

Answer

To solve the expression `45 - (-11) - (-25) + (-42) ? (-3) + 57 + (-4) - (-42)`, we need to determine the value that should replace the question mark (?) to make both sides equal.

### Step-by-Step Solution:

1. **Evaluate the Left Side**:
We start with the left side of the equation:
\[ 45 - (-11) - (-25) + (-42) \]
- First, simplify the double negatives:
- \( -(-11) = +11 \)
- \( -(-25) = +25 \)
- Now, rewrite the expression:
\[ 45 + 11 + 25 - 42 \]

2. **Perform the Addition and Subtraction**:
- First, add \( 45 + 11 \):
\[ 45 + 11 = 56 \]
- Next, add \( 56 + 25 \):
\[ 56 + 25 = 81 \]
- Finally, subtract \( 42 \):
\[ 81 - 42 = 39 \]
- So, the left side equals \( 39 \).

3. **Evaluate the Right Side**:
Now, we evaluate the right side of the equation:
\[ (-3) + 57 + (-4) - (-42) \]
- Again, simplify the double negative:
- \( -(-42) = +42 \)
- Rewrite the expression:
\[ -3 + 57 - 4 + 42 \]

4. **Perform the Addition and Subtraction**:
- First, add \( -3 + 57 \):
\[ -3 + 57 = 54 \]
- Next, subtract \( 4 \):
\[ 54 - 4 = 50 \]
- Finally, add \( 42 \):
\[ 50 + 42 = 92 \]
- So, the right side equals \( 92 \).

5. **Set the Left Side Equal to the Right Side**:
Now we have:
\[ 39 ? 92 \]
To find the correct operation that makes this true, we can check the options:
- If we replace the question mark with \( + \):
\[ 39 + 92 = 131 \quad \text{(not equal)} \]
- If we replace the question mark with \( - \):
\[ 39 - 92 = -53 \quad \text{(not equal)} \]
- If we replace the question mark with \( \times \):
\[ 39 \times 92 = 3588 \quad \text{(not equal)} \]
- If we replace the question mark with \( \div \):
\[ 39 \div 92 \quad \text{(not equal)} \]
- The only operation that makes sense is to check if the question mark represents an equal sign, which means we need to find the value that would make the left side equal to the right side.

### Conclusion:
The correct option to replace the question mark is **B**, which represents the equality between the two sides.