The converse of the statement "If a < b then x + a < x + b ", is

Options

A. If a `gt` b then x + a `lt ` x + b
B. If a `ge` b then x + a `ge` x + b
C. If x + a `lt ` x + b then a `lt` b
D. If x + a `ge` x + b then a `ge` b

Answer

To find the converse of the statement "If a < b then x + a < x + b", we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Original Statement**:
The original statement is "If a < b then x + a < x + b". We can denote this as:
- Let \( p \): \( a < b \)
- Let \( q \): \( x + a < x + b \)

2. **Understand the Converse**:
The converse of a statement "If p then q" is "If q then p". Thus, the converse of our statement will be:
- If \( q \) (i.e., \( x + a < x + b \)), then \( p \) (i.e., \( a < b \)).

3. **Write the Converse Statement**:
Therefore, the converse of the given statement is:
- "If \( x + a < x + b \) then \( a < b \)".

4. **Check the Options**:
We need to check which option matches our converse statement:
- **Option 1**: If \( a > b \) then it is not greater than \( b \). (Incorrect)
- **Option 2**: If \( a \geq b \) then it is also wrong. (Incorrect)
- **Option 3**: If \( x + a < x + b \) then \( a < b \). (Correct)
- **Option 4**: If \( x + a \geq x + b \) then \( a \geq b \). (Incorrect)

5. **Conclusion**:
The correct answer is Option 3: "If \( x + a < x + b \) then \( a < b \)".