Question

ПОМОГИТЕ РЕШИТЬ!Рациональные неравенства 1) 0.3≤0.5+0,1x≤0.6 2)0.1≤0.1x-0.8≤0.5 3)2x-7/6 +7x-2/3 ≤ 3- 1-x/3 4)x2-2x≤2 5)0.8x2≤x+0.3 6)x2-1 2/x-2/3<0

Answer 1

Решение на фото во вложении.
№ 3 непонятно написан, поэтому 2 варианта записи и решения.
№ 6 вообще непонятно написан.

Answer 2

1) 0.3≤0.5+0,1x≤0.6
-0,2≤0,1x≤0,1
-2≤x≤1
x∈[-2;1]

2)0.1≤0.1x-0.8≤0.5
0,9≤0,1x≤1,3
9≤x≤13
x∈[9;13]

3)2x-7/6 +7x-2/3 ≤ 3- 1-x/3
12x-7+42x-4≤18-6-2x
54x+2x≤12+11
-52x≤23
x≥23/52
x∈[23/52;∞)
-----------------------------------
(2x-7)/6+(7x-2)/3≤3-(1-x)/3
2x-7+14x-6≤18-2+2x
16x-2x≤16+13
14x≤27
x≤27/14
x∈(-∞;27/14]

4)x2-2x≤2
x²-2x-2≤0
D=4+8=12
x1=(2-2√3/2=1-√3 U x2=1+√3
x∈[1-√3;1+√3]

5)0.8x2≤x+0.3
0,8x²-x-0,3≤0
8x²-10x-3≤0
D=100+96=196
x1=(10-14)/16=-1/4 U x2=(10+14)/16=1,5
x∈[-0,25;1,5]

6)x2-1 2/x-2/3<0
не поняла запись

Answer 3

1. 0.3 ≤ 0.5 + 0.1x ≤ 0.6

Subtracting 0.5 from all parts of the inequality gives:

-0.2 ≤ 0.1x ≤ 0.1

Then, dividing all parts by 0.1, we get:

-2 ≤ x ≤ 1

Therefore, the solution to the inequality is -2 ≤ x ≤ 1.

2. 0.1 ≤ 0.1x - 0.8 ≤ 0.5

Adding 0.8 to all parts of the inequality gives:

0.9 ≤ 0.1x ≤ 1.3

Dividing all parts by 0.1, we get:

9 ≤ x ≤ 13

Therefore, the solution to the inequality is 9 ≤ x ≤ 13.

3. 2x - 7/6 + 7x - 2/3 ≤ 3 - 1-x/3

Combining like terms gives:

9x - 13/6 ≤ 8/3 - x/3

Multiplying all parts by 3 gives:

27x - 13 ≤ 8 - x

Adding x and 13 to all parts of the inequality gives:

28x ≤ 21

Dividing all parts by 28 gives:

x ≤ 21/28

Therefore, the solution to the inequality is x ≤ 21/28.

4. x^2 - 2x ≤ 2

Moving all parts of the inequality to one side gives:

x^2 - 2x - 2 ≤ 0

Using the quadratic formula gives:

x = (2 ± sqrt(4 + 8)) / 2 = 1 ± sqrt(3)

Therefore, the solution to the inequality is (1 - sqrt(3)) ≤ x ≤ (1 + sqrt(3)).

5. 0.8x^2 ≤ x + 0.3

Moving all parts of the inequality to one side gives:

0.8x^2 - x - 0.3 ≤ 0

Using the quadratic formula gives:

x = (1 ± sqrt(1 + 9.6)) / 1.6 = 0.25, 1.5

Therefore, the solution to the inequality is 0.25 ≤ x ≤ 1.5.

6. x^2 - 1 2/x - 2/3 < 0

Multiplying both sides of the inequality by x gives:

x^3 - x 2/3 < 2/3

Multiplying both sides of the inequality by 3 gives:

3x^3 - 3x 2 < 2

Adding 6x^2 to both sides of the inequality gives:

3x^3 + 6x^2 - 3x - 2 < 6x^2

Using synthetic division gives:

(3x + 2)(x^2 + 2x - 1) < 6x^2

Solving the quadratic equation gives:

x = (-2 ± sqrt(4 + 4)) / 2 = -1 ± sqrt(2)

Therefore, the solution to the inequality is -1 - sqrt(2) < x < -2/3 or -1 + sqrt(2) < x < -2/3.