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 8.

Answer

To determine whether the statement "x is divisible by 8" 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 the Given Information**:
We know that \( x \) is divisible by 24. This means that there exists some integer \( n \) such that:
\[ x = 24n \]

2. **Breaking Down the Divisibility**:
Since \( 24 \) can be factored into its prime factors, we have:
\[ 24 = 8 \times 3 \]
This indicates that \( 24 \) is divisible by \( 8 \).

3. **Substituting into the Divisibility Condition**:
Now, we will substitute \( x \) into the condition for divisibility by \( 8 \):
\[ x = 24n \implies x = (8 \times 3)n = 8(3n) \]

4. **Analyzing the Result**:
From the equation \( x = 8(3n) \), we can see that \( x \) is expressed as \( 8 \) multiplied by some integer \( (3n) \). Since \( 3n \) is an integer (as \( n \) is an integer), it follows that \( x \) is divisible by \( 8 \).

5. **Conclusion**:
Therefore, we conclude that the statement "x is divisible by 8" must be true.

### Final Answer:
The statement "x is divisible by 8" **must be true**.

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