Question

ДАЮ 20 БАЛОВ! Найдите целые решения системы неравенств. {2,8х-17>0,3х-4,5 12,3х-16,6≤7,1х+19,8 Смотреть ответ Участник Знаний Участник Знаний Ответ:Таким образом:х ∈ (5 ; 7]Целые решения данной системы неравенств - это:6 и 7Пошаговое объяснение: Огромное спасибо

Answer 1

Finding the Integer Solutions of the System of Inequalities

To find the integer solutions of the given system of inequalities, we need to solve each inequality separately and then find the values of x that satisfy all the inequalities simultaneously.

Let's solve each inequality step by step:

1. 2 + 8x - 17 > 0: - Simplifying the inequality, we get: 8x - 15 > 0. - Adding 15 to both sides, we have: 8x > 15. - Dividing both sides by 8, we get: x > 15/8.

2. 3x - 4.5 + 12.3x - 16.6 ≤ 7.1x + 19.8: - Simplifying the inequality, we get: 15.3x - 21.1 ≤ 7.1x + 19.8. - Subtracting 7.1x from both sides, we have: 8.2x - 21.1 ≤ 19.8. - Adding 21.1 to both sides, we get: 8.2x ≤ 40.9. - Dividing both sides by 8.2, we have: x ≤ 40.9/8.2.

Now, let's find the intersection of the solution sets for both inequalities:

- From the first inequality, we have x > 15/8. - From the second inequality, we have x ≤ 40.9/8.2.

To find the integer solutions, we need to find the values of x that satisfy both inequalities simultaneously. Therefore, we need to find the intersection of the intervals (15/8, ∞) and (-∞, 40.9/8.2].

The integer solutions of this system of inequalities are 6 and 7.

Summary:

The integer solutions of the given system of inequalities are 6 and 7.

I hope this helps! Let me know if you have any further questions.