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

4x>7
4 x greater than 7

8x>14
8 x greater than 14

6x<10.5
6 x less than 10.5

1.75x<3.5

Answer 1

To determine which inequality Nora solved based on the provided information about the graph, we can analyze the open circle at 1.75 and the leftward arrow extending beyond negative 10.

The open circle indicates that 1.75 is not included in the solution set, which suggests a "less than" inequality. The leftward arrow indicates that the solution includes all values less than 1.75 (and extends infinitely to the left).

Now, let's check each of the inequalities provided:

1. 4x > 7: This inequality, when solved, gives \( x > 1.75 \). This does not match the graph, as we have an open point at 1.75 and the shading would go to the right.

2. 8x > 14: Solving this gives \( x > 1.75 \) as well, which similarly does not match the graph.

3. 6x < 10.5: Solving this gives \( x < 1.75 \). This matches the graph well because it indicates solutions less than 1.75.

4. 1.75x < 3.5: This simplifies to \( x < 2 \). While part of the solution goes left of 1.75, it would not fully extend leftward beyond negative 10.

Based on the evaluation, the inequality that corresponds with the given graph is:

6x < 10.5.