For these statements, the following is true : x is divisible by 24. For each statement, say whether it must be true, could be true, or cannot be true.
x is divisble by 6.

Answer

To determine whether the statement "x is divisible by 6" must be true, could be true, or cannot be true given that "x is divisible by 24", we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Divisibility by 24**:
Since x is divisible by 24, it means that when x is divided by 24, there is no remainder. This can be expressed mathematically as:
\[ x = 24n \]
where n is an integer.

**Hint**: Remember that a number is divisible by another number if it can be expressed as a product of that number and some integer.

2. **Expressing x in terms of n**:
From the equation \(x = 24n\), we can see that x is a multiple of 24.

3. **Finding if x is divisible by 6**:
To check if x is divisible by 6, we can rewrite x in terms of 6:
\[ x = 24n = (6 \times 4)n = 6(4n) \]
This shows that x can be expressed as 6 multiplied by another integer (4n).

**Hint**: If a number can be expressed as a product of another number and an integer, it is divisible by that number.

4. **Conclusion**:
Since x can be expressed as \(6(4n)\), it follows that x is divisible by 6. Therefore, the statement "x is divisible by 6" must be true.

**Final Statement**: The answer is that the statement "x is divisible by 6" must be true.