Question

1234. Решите неравенства: 1) 10 < 3x +4 < 19; 3) 4 < 3+x < 7; 2) -5< 9 + 2x < 17; 4) -3 < x – 8 <1.

Answer 1

хорошего настроения, удачи

Answer 2

1. To solve the inequality 10 < 3x + 4 < 19, we need to isolate the variable x.

10 < 3x + 4 < 19

Subtract 4 from all parts of the inequality:

10 - 4 < 3x + 4 - 4 < 19 - 4

6 < 3x < 15

Divide all parts of the inequality by 3:

6/3 < 3x/3 < 15/3

2 < x < 5

Therefore, the solution to the inequality is 2 < x < 5.

2. For the inequality -5 < 9 + 2x < 17, we'll follow a similar process:

-5 < 9 + 2x < 17

Subtract 9 from all parts of the inequality:

-5 - 9 < 9 + 2x - 9 < 17 - 9

-14 < 2x < 8

Divide all parts of the inequality by 2:

-14/2 < 2x/2 < 8/2

-7 < x < 4

Therefore, the solution to the inequality is -7 < x < 4.

3. Let's solve the inequality 4 < 3 + x < 7:

4 < 3 + x < 7

Subtract 3 from all parts of the inequality:

4 - 3 < 3 + x - 3 < 7 - 3

1 < x < 4

Therefore, the solution to the inequality is 1 < x < 4.

4. Finally, let's solve the inequality -3 < x - 8 < 1:

-3 < x - 8 < 1

Add 8 to all parts of the inequality:

-3 + 8 < x - 8 + 8 < 1 + 8

5 < x < 9

Therefore, the solution to the inequality is 5 < x < 9.