Question

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

Answer 1

Ответ:

Пошаговое объяснение:

1)10<3x+4

-3x<-6

x>2

3)4<3+x<7

3+x>4, 3+x<7

x>1, x<4

x∈(1,4)

2)-5<9+2x<17

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

x>-7, x<4

x∈(-7,4)

4)-3<x-8

-x<-8+3

-x<-5

x>5

Answer 2

1. To solve the inequality 10 < 3x + 4 < 19, we can solve it in two parts:

First, solve the left inequality: 10 < 3x + 4

Subtract 4 from both sides: 10 - 4 < 3x 6 < 3x

Divide both sides by 3 (remember to flip the inequality since we're dividing by a negative number): 6/3 > x 2 > x

So, the left inequality becomes: x < 2.

Next, solve the right inequality: 3x + 4 < 19

Subtract 4 from both sides: 3x < 19 - 4 3x < 15

Divide both sides by 3: x < 15/3 x < 5

So, the right inequality becomes: x < 5.

Combining the two inequalities, we have: 2 > x and x < 5.

Therefore, the solution to the inequality 10 < 3x + 4 < 19 is 2 > x < 5.

2. To solve the inequality -5 < 9 + 2x < 17:

First, subtract 9 from all parts of the inequality: -5 - 9 < 9 + 2x - 9 < 17 - 9 -14 < 2x < 8

Next, divide all parts of the inequality by 2: -14/2 < 2x/2 < 8/2 -7 < x < 4

Therefore, the solution to the inequality -5 < 9 + 2x < 17 is -7 < x < 4.

3. To solve the inequality 4 < 3 + x < 7:

First, subtract 3 from all parts of the inequality: 4 - 3 < 3 + x - 3 < 7 - 3 1 < x < 4

Therefore, the solution to the inequality 4 < 3 + x < 7 is 1 < x < 4.

4. To solve the inequality -3 < x - 8:

Add 8 to both sides of the inequality: -3 + 8 < x - 8 + 8 5 < x

Therefore, the solution to the inequality -3 < x - 8 is x > 5.