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

x+1.25≥1.25
x plus 1.25 greater-than-or-equal-to 1.25

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

x+0.5<3

Answer 1

To determine which inequality Josie solved based on the number line description, let's analyze the given information and the options:

1. The closed circle at 2.5 indicates that the solution set includes 2.5.
2. The line drawn from the closed circle towards 10 indicates that the values greater than or equal to 2.5 are included in the solution.

Now, let's look at the provided inequalities:

1. x − 1.25 ≤ 1.25: This simplifies to x ≤ 2.5, which does not match the graph showing values greater than 2.5.

2. x + 1.25 ≥ 1.25: This simplifies to x ≥ 0, which does not match the graph since it doesn't indicate a starting point at 2.5.

3. x − 1.25 ≥ 1.25: This simplifies to x ≥ 2.5, which matches perfectly with the closed circle at 2.5 and the arrow pointing towards 10.

4. x + 0.5 < 3: This simplifies to x < 2.5, which is again opposite to what the graph indicates.

Considering the analysis above, the correct inequality that Josie solved is:

x − 1.25 ≥ 1.25.