Use the image to answer the question.

A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked on the number line at 4.5. A line is drawn from the circle toward negative 10 with an arrow at the end.

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

(1 point)
Responses

x−1.5≤3
x minus 1.5 less-than-or-equal-to 3

x+1.25≤5.75
x plus 1.25 less-than-or-equal-to 5.75

x+212<212
x plus 2 Start Fraction 1 over 2 End Fraction less than 2 Start Fraction 1 over 2 End Fraction

x−213<216

1 answer

To determine which inequality Willow solved that corresponds to the graph shown, where the graph has an open circle at 4.5 and extends to negative infinity, we need to analyze the options provided:

  1. x − 1.5 ≤ 3
    This inequality rearranges to x ≤ 4.5. The graph would show a closed circle at 4.5 (since it includes 4.5) and would extend left. This does not match the open circle shown.

  2. x + 1.25 ≤ 5.75
    This inequality rearranges to x ≤ 4.5. Similarly, this would indicate a closed circle at 4.5, which does not match the open circle shown.

  3. x + 2.5 < 2.5
    This inequality rearranges to x < 0. The graph would show a closed circle at 0 extending leftward but does not match the circle at 4.5.

  4. x − 2.13 < 2.16
    This inequality rearranges to x < 4.29, which suggests that it would include values less than approximately 4.29 and would have a closed circle on that number. However, it also would not be consistent with having an open circle at 4.5.

None of the options presented seem to match correctly with the open circle at 4.5 and an arrow extending to the left on the number line. However, based on the closest relation to Willow's statement of the inequality and the provided options, the best reasonable conclusion is that she solved an inequality that has an open circle at approximately 4.5, and the appropriate choice should be:

x − 1.5 < 3 (where 4.5 is where x < 4.5)

Thus, the inequality that Willow likely solved is closest to x − 1.5 < 3.