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7. Розв'яжіть нерівність \( |3-4 x|<8 . \quad \) * 1 балл у відповідь запишіть кількість її цілих розв'язків. 2 3 4 4 5

Ask by Davey Schneider. in Germany
Jan 24,2025

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Количество целых решений равно 4.

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Количество целых решений неравенства \( |3 - 4x| < 8 \) равно **4**.

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Щоб розв'язати нерівність \( |3-4 x|<8 \), спершу розділимо на два випадки. 1. \( 3-4x < 8 \) та \( 3-4x > -8 \). Розв'язуючи перший випадок: \[ 3-4x < 8 \Rightarrow -4x < 5 \Rightarrow x > -\frac{5}{4}. \] Розв'язуючи другий випадок: \[ 3-4x > -8 \Rightarrow -4x > -11 \Rightarrow x < \frac{11}{4}. \] Таким чином, ми отримаємо розв'язок: \[ -\frac{5}{4} < x < \frac{11}{4}. \] Тепер знаходимо цілі числа, які належать цьому проміжку: -1, 0, 1, 2. Отже, їх чотири. Відповідь: 4.

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