If 42x is divisible by 9, find the value of digit x.

Answer

To find the value of the digit \( x \) in the number \( 42x \) such that it is divisible by 9, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Rule for Divisibility by 9**: A number is divisible by 9 if the sum of its digits is also divisible by 9.

2. **Identify the Digits**: In the number \( 42x \), the digits are 4, 2, and \( x \).

3. **Calculate the Sum of the Digits**: The sum of the digits can be expressed as:
\[ 4 + 2 + x = 6 + x \]

4. **Set Up the Condition for Divisibility**: For \( 42x \) to be divisible by 9, the sum \( 6 + x \) must be divisible by 9.

5. **Test Possible Values for \( x \)**: The possible values for \( x \) (since \( x \) is a single digit) are from 0 to 9. We will check each value:
- If \( x = 0 \): \( 6 + 0 = 6 \) (not divisible by 9)
- If \( x = 1 \): \( 6 + 1 = 7 \) (not divisible by 9)
- If \( x = 2 \): \( 6 + 2 = 8 \) (not divisible by 9)
- If \( x = 3 \): \( 6 + 3 = 9 \) (divisible by 9)
- If \( x = 4 \): \( 6 + 4 = 10 \) (not divisible by 9)
- If \( x = 5 \): \( 6 + 5 = 11 \) (not divisible by 9)
- If \( x = 6 \): \( 6 + 6 = 12 \) (not divisible by 9)
- If \( x = 7 \): \( 6 + 7 = 13 \) (not divisible by 9)
- If \( x = 8 \): \( 6 + 8 = 14 \) (not divisible by 9)
- If \( x = 9 \): \( 6 + 9 = 15 \) (not divisible by 9)

6. **Conclusion**: The only value of \( x \) that makes \( 6 + x \) divisible by 9 is \( x = 3 \).

### Final Answer:
The value of digit \( x \) is \( 3 \).

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