Question

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

(1 point)

8x>14
8 x greater than 14

1.75x<3.5
1.75 x less than 3.5

6x<10.5
6 x less than 10.5

4x>7

Answer 1

Let's solve each inequality one by one to determine which one Nora might have solved, keeping in mind that we would be looking for a correct solution that she could graph on a number line.

1. **8x > 14**
- Divide both sides by 8:
\[
x > \frac{14}{8} = \frac{7}{4} = 1.75
\]
- The solution is \( x > 1.75 \).

2. **1.75x < 3.5**
- Divide both sides by 1.75:
\[
x < \frac{3.5}{1.75} = 2
\]
- The solution is \( x < 2 \).

3. **6x < 10.5**
- Divide both sides by 6:
\[
x < \frac{10.5}{6} = 1.75
\]
- The solution is \( x < 1.75 \).

4. **4x > 7**
- Divide both sides by 4:
\[
x > \frac{7}{4} = 1.75
\]
- The solution is \( x > 1.75 \).

Based on the solutions:
- The first inequality gives \( x > 1.75 \).
- The second inequality gives \( x < 2 \).
- The third inequality gives \( x < 1.75 \).
- The fourth inequality gives \( x > 1.75 \).

Thus, the inequalities that result in the same kind of solutions would be 1 and 4, both of which state \( x > 1.75 \). The other choices represent different ranges.

From the options provided, if we were to consider the commonality among inequalities, both "8x > 14" and "4x > 7" yield \( x > 1.75 \) as solutions.

If the graph on the number line indicates an open circle on 1.75 and shading to the right, then Nora could have solved either "8x > 14" or "4x > 7".

Without specific details about the graph she produced, it's hard to choose definitively between these two. If we should select just one, I recommend **4x > 7**, as it aligns more directly as a statement related to displaying a simple inequality involving integers.

In conclusion, based on the given inequalities and solutions:

**The answer is: 4x > 7.**