For integers x and y such that xy=14, which of the following is NOT a possible value of x ?

Options

A. 2
B. 1
C. `-7`
D. `-8`

Answer

To solve the problem, we need to determine which of the given options is NOT a possible value of \( x \) when \( xy = 14 \) for integers \( x \) and \( y \).

### Step-by-Step Solution:

1. **Identify the equation**: We start with the equation \( xy = 14 \).

2. **Find the factors of 14**: The integer factors of 14 are:
- Positive factors: 1, 2, 7, 14
- Negative factors: -1, -2, -7, -14

Thus, the complete set of integer pairs \((x, y)\) that satisfy \( xy = 14 \) includes:
- (1, 14)
- (2, 7)
- (7, 2)
- (14, 1)
- (-1, -14)
- (-2, -7)
- (-7, -2)
- (-14, -1)

3. **Evaluate the options**:
- **Option 1: 2**:
- If \( x = 2 \), then \( y = \frac{14}{2} = 7 \). Both are integers. So, this is a possible value.
- **Option 2: 1**:
- If \( x = 1 \), then \( y = \frac{14}{1} = 14 \). Both are integers. So, this is a possible value.
- **Option 3: -7**:
- If \( x = -7 \), then \( y = \frac{14}{-7} = -2 \). Both are integers. So, this is a possible value.
- **Option 4: -8**:
- If \( x = -8 \), then \( y = \frac{14}{-8} = -\frac{14}{8} = -\frac{7}{4} \), which is not an integer. Thus, this is NOT a possible value.

4. **Conclusion**: The option that is NOT a possible value of \( x \) is **Option 4: -8**.

### Final Answer:
The value of \( x \) that is NOT possible is **-8**.