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.
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8x > 14
- Divide both sides by 8: \[ x > \frac{14}{8} = \frac{7}{4} = 1.75 \]
- The solution is \( x > 1.75 \).
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1.75x < 3.5
- Divide both sides by 1.75: \[ x < \frac{3.5}{1.75} = 2 \]
- The solution is \( x < 2 \).
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6x < 10.5
- Divide both sides by 6: \[ x < \frac{10.5}{6} = 1.75 \]
- The solution is \( x < 1.75 \).
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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.
7 answers