Let x represent the difference between the number of heads and the numbers of tails obtained when a coin is tossed 4 times. Then possible values of X is

Answer

To solve the problem, we need to find the possible values of \( x \), which represents the difference between the number of heads and the number of tails when a coin is tossed 4 times.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( M \) be the number of heads obtained when the coin is tossed 4 times. Since there are only heads and tails, the number of tails \( N \) can be expressed as \( N = 4 - M \).

2. **Express \( x \)**:
The difference \( x \) between the number of heads and the number of tails can be expressed as:
\[ x = M - N = M - (4 - M) = 2M - 4 \]

3. **Determine Possible Values of \( M \)**:
Since the coin is tossed 4 times, \( M \) can take values from 0 to 4. Therefore, the possible values of \( M \) are:
\[ M = 0, 1, 2, 3, 4 \]

4. **Calculate \( x \) for Each Value of \( M \)**:
- For \( M = 0 \):
\[ x = 2(0) - 4 = -4 \]
- For \( M = 1 \):
\[ x = 2(1) - 4 = -2 \]
- For \( M = 2 \):
\[ x = 2(2) - 4 = 0 \]
- For \( M = 3 \):
\[ x = 2(3) - 4 = 2 \]
- For \( M = 4 \):
\[ x = 2(4) - 4 = 4 \]

5. **List Possible Values of \( x \)**:
The possible values of \( x \) are:
\[ -4, -2, 0, 2, 4 \]

### Final Answer:
The possible values of \( x \) are \( -4, -2, 0, 2, 4 \).