Question

Willow solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?

(1 point)

x+1.25≤5.75

x−1.5≤3

x+2 1/2<2 1/2

x−2 1/3<2 1/6

Answer 1

To determine which inequality Willow solved, we can analyze each option by simplifying or solving them step-by-step.

1. **x + 1.25 ≤ 5.75**
- Subtract 1.25 from both sides:
\[
x ≤ 5.75 - 1.25 \\
x ≤ 4.5
\]

2. **x - 1.5 ≤ 3**
- Add 1.5 to both sides:
\[
x ≤ 3 + 1.5 \\
x ≤ 4.5
\]

3. **x + 2.5 < 2.5**
- Subtract 2.5 from both sides:
\[
x < 2.5 - 2.5 \\
x < 0
\]

4. **x - 2.33 < 2.16** (since 2 1/3 is approximately 2.33, and 2 1/6 is approximately 2.16)
- Add 2.33 to both sides:
\[
x < 2.16 + 2.33 \\
x < 4.49
\]

After simplifying all the inequalities, we have:

1. \( x ≤ 4.5 \)
2. \( x ≤ 4.5 \)
3. \( x < 0 \)
4. \( x < 4.49 \)

Thus, the inequalities x + 1.25 ≤ 5.75 and x - 1.5 ≤ 3 both simplify to \( x ≤ 4.5 \), while x + 2.5 < 2.5 leads to the solution \( x < 0\) and x - 2.33 < 2.16 leads to \( x < 4.49 \).

If Willow's graph shows a closed circle at 4.5 on the number line (included) or an open circle at values below 0 or below approximated 4.49, you can select the corresponding inequality.

Based on the inequalities and assuming a typical graph representation, the satisfactory choices are:

- **x + 1.25 ≤ 5.75**
- **x - 1.5 ≤ 3**

If required to pick one, either of the first two can be selected based on presentation, but both result in the same graph solution.