Question

Use the image to answer the question.



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 is greater than 14

4x>7
4 x is greater than 7

6x<10.5
6x<10.5

1.75x<3.5

Answer 1

To determine which inequality Nora solved based on the graph of the solution on the number line (though the graph is not provided here), we can analyze each inequality and their potential solutions:

1. **8x > 14**:
\[
\frac{8x}{8} > \frac{14}{8} \implies x > 1.75
\]
This means the solution would be to the right of 1.75 on the number line.

2. **4x > 7**:
\[
\frac{4x}{4} > \frac{7}{4} \implies x > 1.75
\]
Similar to the first, this solution is also to the right of 1.75 on the number line.

3. **6x < 10.5**:
\[
\frac{6x}{6} < \frac{10.5}{6} \implies x < 1.75
\]
This solution would be to the left of 1.75 on the number line.

4. **1.75x < 3.5**:
\[
\frac{1.75x}{1.75} < \frac{3.5}{1.75} \implies x < 2
\]
This solution would be to the left of 2 on the number line.

Based on this evaluation:
- If the solution on the number line marks a point greater than 1.75, it could be either from \(8x > 14\) or \(4x > 7\).
- If the solution marks a point less than 1.75, it would correspond to \(6x < 10.5\).

Since I cannot see the actual graph, you will need to compare these results with the number line Nora used to conclude which inequality she solved.