If a and b are such numbers that `a gt0` and `blt0`, then which one of the following is always correct?

Options

A. `a-bgt0`
B. `a+bgt0`
C. `a+blt0`
D. `a-blt0`

Answer

To solve the problem, we need to analyze the conditions given for the numbers \( a \) and \( b \).

### Step-by-Step Solution:

1. **Understand the Conditions**:
- We know that \( a > 0 \) (a is greater than 0) and \( b < 0 \) (b is less than 0).

2. **Rearranging the Inequalities**:
- Since \( b < 0 \), we can multiply both sides of this inequality by -1. Remember that when we multiply or divide an inequality by a negative number, the direction of the inequality sign flips.
- Thus, multiplying \( b < 0 \) by -1 gives us:
\[ -b > 0 \]

3. **Adding the Inequalities**:
- Now we have two inequalities:
- \( a > 0 \)
- \( -b > 0 \)
- We can add these two inequalities:
\[ a - b > 0 \]
- This means:
\[ a > b \]

4. **Conclusion**:
- From our analysis, we can conclude that \( a - b > 0 \) is always correct given the conditions \( a > 0 \) and \( b < 0 \).

### Final Result:
The statement that is always correct is:
\[ a - b > 0 \]