If x = a, then which of the following is not always true for an integer k.

Options

A. kx = ak
B. `x/k=a/k`
C. x – k = a – k
D. x + k = a + k

Answer

To solve the problem, we need to determine which of the given options is not always true when \( x = a \) and \( k \) is an integer.

### Step-by-Step Solution:

1. **Understand the Given Information**:
We know that \( x = a \). We need to analyze various expressions involving \( k \) (an integer) and see which one fails to hold true for all integers.

2. **Consider Different Options**:
While the specific options are not provided in the question, we can assume they involve operations with \( x \), \( a \), and \( k \). Common forms might include:
- \( x + k = a + k \)
- \( x - k = a - k \)
- \( x \cdot k = a \cdot k \)
- \( \frac{x}{k} = \frac{a}{k} \)

3. **Evaluate Each Option**:
- For \( x + k = a + k \): This is true for all integers \( k \) since both sides simplify to \( a + k \).
- For \( x - k = a - k \): This is also true for all integers \( k \) since both sides simplify to \( a - k \).
- For \( x \cdot k = a \cdot k \): This is true for all integers \( k \) as both sides simplify to \( a \cdot k \).
- For \( \frac{x}{k} = \frac{a}{k} \): This is true for all integers \( k \) except when \( k = 0 \) because division by zero is undefined.

4. **Identify the Incorrect Option**:
The expression \( \frac{x}{k} = \frac{a}{k} \) is not valid when \( k = 0 \) because division by zero is undefined. Therefore, this option is the one that is not always true.

5. **Conclusion**:
The option that is not always true for an integer \( k \) is the one involving division by \( k \).

### Final Answer:
The expression \( \frac{x}{k} = \frac{a}{k} \) is not always true for an integer \( k \) because it is undefined when \( k = 0 \).