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Укажите наибольшее целое число, принадлежащее пересечению числовых промежутков. \[ (-\infty ; 7) \text { и }(-3 ; 9) \]

Ask by Ramos Franklin. in Kazakhstan
Nov 01,2024

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Наибольшее целое число в пересечении числовых промежутков \((- \infty; 7)\) и \((-3; 9)\) — 6.

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Чтобы найти наибольшее целое число, принадлежащее пересечению числовых промежутков \((- \infty; 7)\) и \((-3; 9)\), сначала определим пересечение этих промежутков. 1. Промежуток \((- \infty; 7)\) включает все числа, которые меньше 7. 2. Промежуток \((-3; 9)\) включает все числа, которые больше -3 и меньше 9. Теперь найдем пересечение этих двух промежутков: - Левый конец пересечения: максимальное из -3 и -∞, то есть -3. - Правый конец пересечения: минимальное из 7 и 9, то есть 7. Таким образом, пересечение промежутков будет \((-3; 7)\). Наибольшее целое число, принадлежащее этому промежутку, это 6. Ответ: 6.

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В задании рассматриваются два числовых промежутка: первый \( (-\infty ; 7) \) включает все числа меньше 7, а второй \( (-3 ; 9) \) включает все числа больше -3 и меньше 9. Пересечение этих промежутков будет ограничено обоими условиями. Наибольшее целое число, попадающее в это пересечение, — это 6, поскольку 7 не включено в первый промежуток, а 8 и 9 не попадают во второй. Таким образом, ответ: 6.

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