Question

3) {x < 4, [x < 7;1) (x > 7,1x <10;2) ſx > 3,x < 6;5) J x < -4,(x > 3;Мулл4) (x > -1,(x > 2;6) [x = 0,x > - 5.​ Смотреть ответ Участник Знаний Участник Знаний Пошаговое объяснение: 3) Система неравенств: x<4 x<7 x принадлежит (-∞; 4) 1) Система неравенств: x>7 x<10 x принадлежит (7; 10) 2) Система неравенств: х>3 x<6 x принадлежит (3; 6) 5) Система неравенств: x<-4 x>3 Система не имеет решений. 4) Система неравенств: x>-1 x>2 x принадлежит (2; +∞) 6) Система: x=0 x>-5 x принадлежит [0].

Answer 1

To solve the system of inequalities, let's analyze each inequality separately and find the intersection of their solution sets. Here's the step-by-step explanation for each part:

1. x < 4 This represents all values of x that are less than 4. The solution set is (-∞, 4).

2. x < 7 This represents all values of x that are less than 7. The solution set is (-∞, 7).

3. x > 7, 1 < x < 10 This represents all values of x that are greater than 7 but also less than 10. The solution set is (7, 10).

4. x > 3, x < 6 This represents all values of x that are greater than 3 but also less than 6. The solution set is (3, 6).

5. x < -4, x > 3 Here we have a contradiction because there is no possible value of x that is simultaneously less than -4 and greater than 3. This system has no solution.

6. x > -1, x > 2 This represents all values of x that are greater than both -1 and 2. The solution set is (2, +∞).

7. x = 0, x > -5 This represents two conditions: x must be equal to 0 and also greater than -5. The only value that satisfies both conditions is x = 0.

Now let's find the intersection of these solution sets:

The common solution set among all the inequalities is the intersection of all the individual solution sets:

Intersection of (1), (2), and (3): (7, 10) Intersection of (1), (3), and (4): (7, 10) Intersection of (1), (4), and (6): (2, 4) Intersection of (6) and (7): {2}

So, the final solution set for the system of inequalities is x ∈ {2}. This means the value of x that satisfies all the given conditions is 2.