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НСтв \( \left\{\begin{array}{l}9-2 x \leq-7 \\ -8+3 x \leq 1\end{array}\right. \)

Ask by Park Olson. in Russia
Mar 13,2025

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Ответ: система не имеет решений.

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Bonus Knowledge

Чтобы решить систему неравенств, начнем с первого неравенства: 1. \( 9 - 2x \leq -7 \) Переносим \( 9 \) на правую сторону: \[ -2x \leq -16 \] Разделим обе стороны на \(-2\) (обратите внимание, что знак неравенства сменится на противоположный): \[ x \geq 8 \] Теперь переходим ко второму неравенству: 2. \( -8 + 3x \leq 1 \) Прибавим \( 8 \) к обеим сторонам: \[ 3x \leq 9 \] Разделим на \( 3 \): \[ x \leq 3 \] Теперь у нас есть два результата: \[ x \geq 8 \quad \text{и} \quad x \leq 3 \] Так как \( x \) не может одновременно быть больше или равным 8 и меньше или равным 3, то система неравенств не имеет решения.

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