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

x−2 1/3<2 1/6
x minus 2 Start Fraction 1 over 3 End Fraction less than 2 Start Fraction 1 over 6 End Fraction

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

x+2 1/2<2 1/2

Answer 1

To determine which inequality Willow solved based on the number line description, we need to analyze what the graph represents. The open circle at 4.5 with a line extending to the left toward negative 10 indicates that the solution consists of all values less than 4.5, but not including 4.5 itself. This signifies that the inequality is strictly less than 4.5.

Now, we can examine the given options:

1. x + 1.25 ≤ 5.75:

   • Rearranging gives us \( x ≤ 4.5 \). This would include 4.5 as a solution, hence it doesn't match the graph.

2. x - 2 1/3 < 2 1/6:

   • Simplifying this, we have \( x < 2 1/6 + 2 1/3 = 2 1/6 + 2.3333 \approx 4.5 \). This is a match since it shows values strictly less than 4.5.

3. x - 1.5 ≤ 3:

   • Rearranging gives \( x ≤ 4.5 \). This includes 4.5, which doesn't match the graph.

4. x + 2 1/2 < 2 1/2:

   • This would imply \( x < 0 \), which does not correspond to the number line shown.

Based on the analysis, the correct inequality that matches the graph of all numbers less than 4.5 (with an open circle at 4.5) is:

x - 2 1/3 < 2 1/6.