Use the image to answer the question.

Question

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 1.75. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.

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

(1 point)
Responses

8x>14
8 x greater than 14

6x<10.5
6 x less than 10.5

4x>7
4 x greater than 7

1.75x<3.5

Answer 1

To solve the problem, we need to determine which inequality corresponds to the graphical representation described. The open circle at 1.75 indicates that this value is not included in the solution set, and the leftward arrow signifies that values less than 1.75 are included.

Let's analyze each option:

1. 8x > 14: When solved, this gives \( x > \frac{14}{8} = 1.75 \). This would produce a rightward arrow starting from 1.75, which does not match the open circle and leftward arrow.

2. 6x < 10.5: When solved, this gives \( x < \frac{10.5}{6} = 1.75 \). This would indeed produce a leftward arrow starting from 1.75, which is a match.

3. 4x > 7: When solved, this gives \( x > \frac{7}{4} = 1.75 \). Similar to the first option, this would produce a rightward arrow, which does not match the description.

4. 1.75x < 3.5: When solved, this gives \( x < \frac{3.5}{1.75} = 2 \). This doesn't produce an arrow starting at 1.75, as 2 is not less than 1.75.

The only option that results in a leftward arrow from an open point at 1.75 is:

6x < 10.5