Question

Решите систему неравенств (45-46): 3x - 9> -6, 2x + 5> 4,3 + x; 45. 1) 3) (2,5x+12,4 > 3x - 1,5, 3x - 6,7 < 4,3 + 4,5x; 4x + 7 > x- 5. 3x - 6,7 < 4.3 - 2,5х; (2.4x + 3.6 > 2x - 3.4. 5.4x - 8,7 < 7,3 + 2.4х. помогите пожалуйста плиз ​

Answer 1

Ответ:

Объяснение:

3x-9>-6 ⇒ 3x>-6+9 ⇒ x>3/3 ⇒ x>1

2x+5>4,3+x ⇒ 2x-x>4,3-5 ⇒ x>-0,7

Отсюда следует, x>1.

Ответ: x∈(1; ∞).

2,5x+12,4>3x-1,5 ⇒ 2,5x-3x>-1,5-12,4 ⇒ -0,5x>-13,9 ⇒ x<139/5 ⇒ x<27,8

3x-6,7<4,3+4,5x ⇒ 3x-4,5x<4,3+6,7 ⇒ -1,5x<11 ⇒ x>-110/15 ⇒ x>-7 1/3

-7 1/3<x<27,8

Ответ: x∈(-7 1/3; 27,8).

4x+7>x-5 ⇒ 4x-x>-5-7 ⇒ 3x>-12 ⇒ x>-12/3 ⇒ x>-4

3x-6,7<4,3-2,5x ⇒ 3x+2,5x<4,3+6,7 ⇒ 5,5x<11 ⇒ x<110/55 ⇒ x<2

-4<x<2

Ответ: x∈(-4; 2).

2,4x+3,6>2x-3,4 ⇒ 2,4x-2x>-3,4-3,6 ⇒ 0,4x>-7 ⇒ x>-70/4 ⇒ x>-17,5

5,4x-8,7<7,3+2,4x ⇒ 5,4x-2,4x<7,3+8,7 ⇒ 3x<16 ⇒ x<16/3 ⇒ x<5 1/3

-17,5<x<5 1/3

Ответ: x∈(-17,5; 5 1/3).

Answer 2

Solving the System of Inequalities

To solve the system of inequalities, we will go through each inequality one by one and find the values of x that satisfy each inequality. Then, we will find the intersection of all the solution sets to determine the final solution.

Let's start with the first system of inequalities:

1) (45-46): 3x - 9 > -6 2) 2x + 5 > 4 3) 3 + x; 45

To solve the first inequality, we can simplify it as follows:

(45-46): 3x - 9 > -6 -1: 3x - 9 > -6 3x > 3 x > 1

So, the first inequality can be written as x > 1.

Now, let's solve the second inequality:

2x + 5 > 4 2x > -1 x > -1/2

Therefore, the second inequality can be written as x > -1/2.

Finally, let's solve the third inequality:

3 + x; 45 x; 42

So, the third inequality can be written as x ≤ 42.

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

The first inequality gives us x > 1. The second inequality gives us x > -1/2. The third inequality gives us x ≤ 42.

To find the intersection, we need to find the common values that satisfy all three inequalities. From the given solution sets, we can see that the common solution is x > 1.

Therefore, the solution to the system of inequalities is x > 1.

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