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

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−2 1/3<2 1/6

Answer 1

To determine which inequality corresponds to the described graph, let's analyze the information:

1. The open circle at 4.5 indicates that this value is not included in the solution set.
2. The line extending from the open circle toward negative 10 suggests that the solution includes all values less than 4.5.

Now let's examine each of the provided inequalities:

1. \( x + 2.5 < 2.5 \)

   • To solve: \( x < 2.5 - 2.5 \) → \( x < 0 \)
   • This would graph as an open circle at 0, which does not match.

2. \( x - 1.5 ≤ 3 \)

   • To solve: \( x ≤ 3 + 1.5 \) → \( x ≤ 4.5 \)
   • This includes 4.5 (closed circle), which does not match.

3. \( x + 1.25 ≤ 5.75 \)

   • To solve: \( x ≤ 5.75 - 1.25 \) → \( x ≤ 4.5 \)
   • This also includes 4.5 (closed circle), which does not match.

4. \( x - 2 \frac{1}{3} < 2 \frac{1}{6} \)

   • Converting mixed numbers: \( x - \frac{7}{3} < \frac{13}{6} \)
   • To solve: \( x < \frac{13}{6} + \frac{7}{3} \)
   • Convert \( \frac{7}{3} \) to sixths: \( \frac{7}{3} = \frac{14}{6} \)
   • Combine: \( x < \frac{13}{6} + \frac{14}{6} = \frac{27}{6} \) → \( x < 4.5 \)

This last inequality does correctly correspond with the graph showing values less than 4.5 (open circle).

Therefore, the correct inequality that Willow solved is:

\( x - 2 \frac{1}{3} < 2 \frac{1}{6} \).