To determine which inequality Paolo solved, we need to analyze each option closely, potentially calculating the value of \( x \) in each case.
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For the inequality \( 4.9x > 19.6 \):
- Divide both sides by 4.9: \[ x > \frac{19.6}{4.9} = 4 \]
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For the inequality \( 2.1x < 8.4 \):
- Divide both sides by 2.1: \[ x < \frac{8.4}{2.1} = 4 \]
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For the inequality \( 3.7x > 14.8 \):
- Divide both sides by 3.7: \[ x > \frac{14.8}{3.7} \approx 4 \]
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For the inequality \( 2.8x < 10.5 \):
- Divide both sides by 2.8: \[ x < \frac{10.5}{2.8} \approx 3.75 \]
Now summarizing the results:
- \( 4.9x > 19.6 \) gives the solution \( x > 4 \)
- \( 2.1x < 8.4 \) gives the solution \( x < 4 \)
- \( 3.7x > 14.8 \) gives the solution \( x > 4 \)
- \( 2.8x < 10.5 \) gives the solution \( x < 3.75 \)
If Paolo's graph indicates a solution greater than \( 4 \), then the inequalities he solved would be either \( 4.9x > 19.6 \) or \( 3.7x > 14.8 \).
If the graph shows a solution less than \( 4 \), it could be \( 2.1x < 8.4 \) or \( 2.8x < 10.5 \); specifically, the latter would be less than \( 3.75 \).
From the options available, without the graph itself, we cannot definitively determine which inequality Paolo solved, but based on logical deductions:
- If the graph shows values greater than 4, Paolo solved either \( 4.9x > 19.6 \) or \( 3.7x > 14.8 \).
- If the graph shows values less than 4, he solved either \( 2.1x < 8.4 \) or \( 2.8x < 10.5\).
To accurately answer, we would need to know the type of solutions indicated on the graph. If you have that information, please provide it.