Use the image to answer the question.

Question

A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the number line at 2.5. A line is drawn from the closed circle toward 10 with an arrow at the end.
Josie solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?

(1 point)
Responses

x+0.5<3
x plus 0.5 less-than 3

x−1.25≤1.25
x minus 1.25 less-than-or-equal-to 1.25

x−1.25≥1.25
x minus 1.25 greater-than-or-equal-to 1.25

x+1.25≥1.25

Answer 1

To determine which inequality Josie solved based on the described number line, we know that there is a closed circle at 2.5, and the line extends from 2.5 towards 10.

1. The closed circle at 2.5 indicates that 2.5 is included in the solution set. Thus, the inequality must be greater than or greater than or equal to.
2. The line extending towards 10 indicates the solution includes all numbers greater than or equal to 2.5.

Now let's analyze the given inequalities:

1. x + 0.5 < 3

   • Solving for x: \[ x < 3 - 0.5 \Rightarrow x < 2.5 \]
   • This does not match the representation on the number line.

2. x − 1.25 ≤ 1.25

   • Solving for x: \[ x ≤ 1.25 + 1.25 \Rightarrow x ≤ 2.5 \]
   • This would be a closed circle at 2.5, but it includes all values less than or equal to 2.5, which does not match the number line description that extends to 10.

3. x − 1.25 ≥ 1.25

   • Solving for x: \[ x ≥ 1.25 + 1.25 \Rightarrow x ≥ 2.5 \]
   • This is consistent with a closed circle at 2.5 and extending towards 10.

4. x + 1.25 ≥ 1.25

   • Solving for x: \[ x ≥ 1.25 - 1.25 \Rightarrow x ≥ 0 \]
   • This would create a range starting at 0, which does not match the representation on the number line.

Given this analysis, the correct inequality that Josie solved is:

x − 1.25 ≥ 1.25.