The sum of 4.5 and one-third a number is equal to at most 38.9. What are all the possible values of the number? How would you write an inequality that could be used to solve this problem?

To find all possible values of the number, let's denote the unknown number as \( x \).

According to the problem, the sum of \( 4.5 \) and one-third of \( x \) is equal to at most \( 38.9 \). This can be expressed as the following inequality:

\[ 4.5 + \frac{1}{3}x \leq 38.9 \]

Now, we can solve the inequality for \( x \).

1. Start by isolating \(\frac{1}{3}x\): \[ \frac{1}{3}x \leq 38.9 - 4.5 \]

2. Calculate \( 38.9 - 4.5 \): \[ 38.9 - 4.5 = 34.4 \]

3. Now the inequality is: \[ \frac{1}{3}x \leq 34.4 \]

4. Multiply both sides by \( 3 \) to solve for \( x \): \[ x \leq 34.4 \times 3 \]

5. Calculate \( 34.4 \times 3 \): \[ 34.4 \times 3 = 103.2 \]

Thus, the solution to the inequality is: \[ x \leq 103.2 \]

Therefore, the possible values of the number \( x \) are all real numbers that are less than or equal to \( 103.2 \). The final answer is:

\[ x \in (-\infty, 103.2] \]