Question

4. 1) К каждой стороне неравенства х≥ 6 прибавьте числа -5, 6, -3, 11 2) К каждой стороне неравенства х-3<9 прибавьте числа 3; -6,9,-7. Запишите результаты.С решением пожалуйста дам 40 баллов

Answer 1

Ответ:

x+3≥18:

Прибавляем -5: x+3-5 ≥ 18-5 => x-2 ≥ 13

Прибавляем 6: x+3+6 ≥ 18+6 => x+9 ≥ 24

Прибавляем -3: x+3-3 ≥ 18-3 => x ≥ 15

Прибавляем 11: x+3+11 ≥ 18+11 => x+14 ≥ 29

Ответ:

x-2 ≥ 13, x+9 ≥ 24, x ≥ 15, x+14 ≥ 29

х-3<9:

Прибавляем 3: x-3+3 < 9+3 => x < 12

Прибавляем -6: x-3-6 < 9-6 => x-9 < 3

Прибавляем 9: x-3+9 < 9+9 => x+6 < 18

Прибавляем -7: x-3-7 < 9-7 => x-10 < 2

Ответ:

x < 12, x-9 < 3, x+6 < 18, x-10 < 2

Answer 2

1) To solve the inequality x ≥ 6, we need to add the numbers -5, 6, -3, and 11 to both sides of the inequality.

Adding -5 to both sides: x + (-5) ≥ 6 + (-5) simplifies to x - 5 ≥ 1. Adding 6 to both sides: x - 5 + 6 ≥ 1 + 6 simplifies to x + 1 ≥ 7. Adding -3 to both sides: x + 1 + (-3) ≥ 7 + (-3) simplifies to x - 2 ≥ 4. Adding 11 to both sides: x - 2 + 11 ≥ 4 + 11 simplifies to x + 9 ≥ 15.

Therefore, the result of adding -5, 6, -3, and 11 to both sides of the inequality x ≥ 6 is x + 9 ≥ 15.

2) To solve the inequality x - 3 < 9, we need to add the numbers 3, -6, 9, and -7 to both sides of the inequality.

Adding 3 to both sides: x - 3 + 3 < 9 + 3 simplifies to x < 12. Adding -6 to both sides: x + (-6) < 12 + (-6) simplifies to x - 6 < 6. Adding 9 to both sides: x - 6 + 9 < 6 + 9 simplifies to x + 3 < 15. Adding -7 to both sides: x + 3 + (-7) < 15 + (-7) simplifies to x - 4 < 8.

Therefore, the result of adding 3, -6, 9, and -7 to both sides of the inequality x - 3 < 9 is x - 4 < 8.

The results of the two inequalities are: 1) x + 9 ≥ 15 2) x - 4 < 8

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