Question

he sum of 4.5 and one third a number is equal to at most 38.9. what are all the possile values of the number? how would you write an inequality that could be used to solve this problem?

Answer 1

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.

1. First, subtract \( 4.5 \) from both sides:

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

2. Calculate the right side:

\[
\frac{1}{3}x \leq 34.4
\]

3. Now, to isolate \( x \), multiply both sides by \( 3 \):

\[
x \leq 3 \times 34.4
\]

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 \( (-\infty, 103.2] \).