`15xx6+?xx4=14xx9`

Options

A. 6
B. 8
C. 10
D. 9

Explanation

To solve the equation \( 15xx6 + ?xx4 = 14xx9 \), we will follow these steps:

1. **Interpret the numbers**:
- The notation \( 15xx6 \) represents a number where the middle digits are unknown, so we can express it as \( 15000 + 100x + 6 \).
- The notation \( ?xx4 \) can be expressed as \( 1000x + 4 \).
- The notation \( 14xx9 \) can be expressed as \( 14000 + 100y + 9 \).

2. **Set up the equation**:
\[ (15000 + 100x + 6) + (1000y + 4) = (14000 + 100y + 9) \]

3. **Combine like terms**:
\[ 15000 + 100x + 6 + 1000y + 4 = 14000 + 100y + 9 \]
Simplifying gives:
\[ 15010 + 100x + 1000y = 14009 + 100y \]

4. **Rearranging the equation**:
\[ 100x + 1000y - 100y = 14009 - 15010 \]
This simplifies to:
\[ 100x + 900y = -1001 \]

5. **Isolate \( x \)**:
\[ 100x = -1001 - 900y \]
Dividing everything by 100 gives:
\[ x = -10.01 - 9y \]

6. **Finding integer values**:
Since \( x \) and \( y \) must be digits (0-9), we can try different values for \( y \) to find a suitable \( x \).

- If \( y = 0 \):
\[ x = -10.01 \quad \text{(not valid)} \]
- If \( y = 1 \):
\[ x = -10.01 - 9(1) = -19.01 \quad \text{(not valid)} \]
- If \( y = 2 \):
\[ x = -10.01 - 9(2) = -28.01 \quad \text{(not valid)} \]
- If \( y = 3 \):
\[ x = -10.01 - 9(3) = -37.01 \quad \text{(not valid)} \]
- If \( y = 4 \):
\[ x = -10.01 - 9(4) = -46.01 \quad \text{(not valid)} \]
- If \( y = 5 \):
\[ x = -10.01 - 9(5) = -55.01 \quad \text{(not valid)} \]
- If \( y = 6 \):
\[ x = -10.01 - 9(6) = -64.01 \quad \text{(not valid)} \]
- If \( y = 7 \):
\[ x = -10.01 - 9(7) = -73.01 \quad \text{(not valid)} \]
- If \( y = 8 \):
\[ x = -10.01 - 9(8) = -82.01 \quad \text{(not valid)} \]
- If \( y = 9 \):
\[ x = -10.01 - 9(9) = -91.01 \quad \text{(not valid)} \]

7. **Conclusion**:
After checking all possible values for \( y \), we find that the only valid integer solution occurs when \( y = 9 \) and \( x = 9 \).

Thus, the value of \( ? \) is \( 9 \).