To translate the problem into a mathematical inequality, let \( x \) represent the unknown number. According to the problem, the sum of \( 4.5 \) and one third of \( x \) must be less than or equal to \( 38.9 \). We can express this as:
\[ 4.5 + \frac{1}{3}x \leq 38.9 \]
Next, we will solve this inequality step-by-step.
- First, subtract \( 4.5 \) from both sides:
\[ \frac{1}{3}x \leq 38.9 - 4.5 \]
- Calculate the right side:
\[ \frac{1}{3}x \leq 34.4 \]
- Now, to isolate \( x \), multiply both sides by \( 3 \):
\[ x \leq 3 \times 34.4 \]
- Calculate \( 3 \times 34.4 \):
\[ x \leq 103.2 \]
So, the inequality that represents all possible values of the number \( x \) is:
\[ x \leq 103.2 \]
This means that \( x \) can take any value that is less than or equal to \( 103.2 \). All possible values of the number \( x \) are in the range \( (-\infty, 103.2] \).
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