If 3x72 is divisible by 3, find the value of x.

Answer

To find the value of \( x \) in the expression \( 3x72 \) such that it is divisible by 3, we can follow these steps:

### Step 1: Understand the divisibility rule for 3
A number is divisible by 3 if the sum of its digits is divisible by 3.

### Step 2: Identify the digits in the number
The number \( 3x72 \) consists of the digits 3, \( x \), 7, and 2.

### Step 3: Write the expression for the sum of the digits
The sum of the digits is:
\[ 3 + x + 7 + 2 \]

### Step 4: Simplify the sum
Combine the known digits:
\[ 3 + 7 + 2 = 12 \]
So, the sum becomes:
\[ 12 + x \]

### Step 5: Set up the divisibility condition
For \( 3x72 \) to be divisible by 3, \( 12 + x \) must also be divisible by 3.

### Step 6: Check the values of \( x \)
Now we will check the possible values of \( x \) (from 0 to 9) to see which make \( 12 + x \) divisible by 3.

- If \( x = 0 \): \( 12 + 0 = 12 \) (divisible by 3)
- If \( x = 1 \): \( 12 + 1 = 13 \) (not divisible by 3)
- If \( x = 2 \): \( 12 + 2 = 14 \) (not divisible by 3)
- If \( x = 3 \): \( 12 + 3 = 15 \) (divisible by 3)
- If \( x = 4 \): \( 12 + 4 = 16 \) (not divisible by 3)
- If \( x = 5 \): \( 12 + 5 = 17 \) (not divisible by 3)
- If \( x = 6 \): \( 12 + 6 = 18 \) (divisible by 3)
- If \( x = 7 \): \( 12 + 7 = 19 \) (not divisible by 3)
- If \( x = 8 \): \( 12 + 8 = 20 \) (not divisible by 3)
- If \( x = 9 \): \( 12 + 9 = 21 \) (divisible by 3)

### Step 7: List the valid values of \( x \)
The values of \( x \) that make \( 12 + x \) divisible by 3 are:
- \( x = 0 \)
- \( x = 3 \)
- \( x = 6 \)
- \( x = 9 \)

### Conclusion
Thus, the possible values of \( x \) are \( 0, 3, 6, \) and \( 9 \).

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