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?(1 point)

Question

Responses

Answer 1

Let the unknown number be represented by \( x \). According to the problem, the sum of 4.5 and one-third of the number is at most 38.9. This can be expressed with the following inequality:

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

To solve this inequality for \( x \), follow these steps:

1. Subtract 4.5 from both sides:

   \[ \frac{1}{3}x \leq 38.9 - 4.5 \] \[ \frac{1}{3}x \leq 34.4 \]

2. Multiply both sides by 3 to isolate \( x \):

   \[ x \leq 34.4 \times 3 \] \[ x \leq 103.2 \]

Thus, the solution set for \( x \) is:

\[ x \leq 103.2 \]

Therefore, all possible values of the number \( x \) are those that satisfy the inequality \( x \leq 103.2 \).