Let's break down the statement step by step to determine the date.
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"the day before yesterday": Let's call today \( T \). The day before yesterday would be \( T - 2 \).
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"8 days after the day before yesterday": This would be \( (T - 2) + 8 = T + 6 \).
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"the day before" that: This means we go one day back from \( T + 6 \), which is \( (T + 6) - 1 = T + 5 \).
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"4 days before" that: Now we subtract 4 days from \( T + 5 \), which yields \( (T + 5) - 4 = T + 1 \).
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"one day after" that: Next, we add one day, resulting in \( (T + 1) + 1 = T + 2 \).
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"six days before" that: Finally, we subtract 6 days from \( T + 2 \), giving us \( (T + 2) - 6 = T - 4 \).
So the original statement boils down to saying that July 7 was \( T - 4 \). This means:
\[ T - 4 = \text{July 7} \]
To find \( T \), we can express this as:
\[ T = \text{July 7} + 4 \text{ days} \]
Calculating \( T \):
- July 8 (1 day after July 7)
- July 9 (2 days after July 7)
- July 10 (3 days after July 7)
- July 11 (4 days after July 7)
Thus, today is July 11.
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