Question

№954 1) 2(3х+1)-х≤ 3(х+4)2) 7х+4(х-2)> 6(1+3х)3) 2(х-1)-3(х+2)≤ 6(1+х)4) 7(у+3)-2(у+2)≥2(5у+1)5) 6(3+5у)-(2+7у)≤5(4+3у)6) 4(3у-1)-3(у-1)>2(3+у)пж пж пж ​

Answer 1

Ответ:

Пошаговое объяснение:

1) 2(3х+1)-х≤ 3(х+4)

6x+2-x≤3x+12

6x-x-3x≤12-2

2x≤10

x≤5

2) 7х+4(х-2)> 6(1+3х)

7x+4x-8>6+18x

7x+4x-18x>6+8

-7x>14

x<-2

3)2(х-1)-3(х+2)≤ 6(1+х)

2x-2-3x-6≤6+6x

2x-3x-6x≤6+6+2

-7x≤14

x≥-2

4)7(у+3)-2(у+2)≥2(5у+1)

7y+21-2y-4≥10y+2

7y-2y-10y≥2+4-21

-5y≥-15

y≤3

5) 6(3+5у)-(2+7у)≤5(4+3у)

18+30y-2-7y≤20+15y

30y-7y-15y≤20-18+2

8y≤4

y≤1/2

6) 4(3у-1)-3(у-1)>2(3+у)

12y-4-3y+3>6+2y

12y-3y-2y>6+4-3

7y>7

y>1

Answer 2

Ответ:

Пошаговое о1) 2(3x + 1) - x ≤ 3(x + 4),                   2) 7x + 4(x - 2) > 6(1 + 3x),

 6х + 2 - х ≤ 3х + 12,                           7х + 4х - 8 > 6 + 18x,

 5х + 2 ≤ 3х + 12,                                11x - 8 > 6 + 18x,

 5х - 3х ≤ 12 - 2,                                  11x - 18x > 6 + 8,

 2х ≤ 10,                                               -7x > 14,

 х ≤ 5,                                                   x < - 2,

 х ∈ (-∞; 5];                                            x ∈ (-∞; -2);

3) 2(x - 1) - 3(x + 2) < 6(1 + x),              4) 7(y + 3) - 2(y + 2) ≥ 2(5y + 1),

   2x - 2 - 3x - 6 < 6 + 6x,                      7y + 21 - 2y - 4 ≥ 10y + 2,

   -x - 8 < 6 + 6x,                                    5y + 17 ≥ 10y + 2,

   -x - 6x < 6 + 8,                                     5y - 10y ≥ 2 - 17,

   -7x < 14,                                                -5y ≥ -15,

   x > -2,                                                   y ≤ 3,

   x ∈ (-2; +∞);                                           y ∈ (-∞; 3]. бъяснение:

Answer 3

To solve these inequalities, we'll work through each one step by step:

1. 2(3x+1) - x ≤ 3(x+4)

First, distribute the constants on both sides of the inequality:

6x + 2 - x ≤ 3x + 12

Combine like terms:

5x + 2 ≤ 3x + 12

Now, isolate x by moving 3x to the left side of the inequality:

5x - 3x + 2 ≤ 12

2x + 2 ≤ 12

Subtract 2 from both sides:

2x ≤ 10

Now, divide by 2:

x ≤ 5

2. 7x + 4(x-2) > 6(1+3x)

First, distribute the constants on both sides of the inequality:

7x + 4x - 8 > 6 + 18x

Combine like terms:

11x - 8 > 6 + 18x

Now, isolate x by moving 18x to the left side of the inequality:

11x - 18x - 8 > 6

-7x - 8 > 6

Add 8 to both sides:

-7x > 14

Now, divide by -7 (note that when you divide by a negative number, the inequality sign flips):

x < -2

3. 2(x-1) - 3(x+2) ≤ 6(1+x)

First, distribute the constants on both sides of the inequality:

2x - 2 - 3x - 6 ≤ 6 + 6x

Combine like terms:

-1x - 8 ≤ 6 + 6x

Now, isolate x by moving 6x to the left side of the inequality:

-1x - 6x - 8 ≤ 6

-7x - 8 ≤ 6

Add 8 to both sides:

-7x ≤ 14

Now, divide by -7:

x ≥ -2

4. 7(y+3) - 2(y+2) ≥ 2(5y+1)

First, distribute the constants on both sides of the inequality:

7y + 21 - 2y - 4 ≥ 10y + 2

Combine like terms:

5y + 17 ≥ 10y + 2

Now, isolate y by moving 10y to the left side of the inequality:

5y - 10y + 17 ≥ 2

-5y + 17 ≥ 2

Subtract 17 from both sides:

-5y ≥ -15

Now, divide by -5 (note that when you divide by a negative number, the inequality sign flips):

y ≤ 3

5. 6(3+5y) - (2+7y) ≤ 5(4+3y)

First, distribute the constants on both sides of the inequality:

18 + 30y - 2 - 7y ≤ 20 + 15y

Combine like terms:

18 + 30y - 2 - 7y ≤ 20 + 15y

Now, isolate y by moving 15y to the left side of the inequality:

30y - 7y - 15y ≤ 20 - 2

8y - 15y ≤ 18

-7y ≤ 18

Divide by -7 (note that when you divide by a negative number, the inequality sign flips):

y ≥ -18/7

6. 4(3y-1) - 3(y-1) > 2(3+y)

First, distribute the constants on both sides of the inequality:

12y - 4 - 3y + 3 > 6 + 2y

Combine like terms:

9y - 1 > 6 + 2y

Now, isolate y by moving 2y to the left side of the inequality:

9y - 2y - 1 > 6

7y - 1 > 6

Add 1 to both sides:

7y > 7

Divide by 7:

y > 1

So, the solutions to the inequalities are:

1. x ≤ 5
2. x < -2
3. x ≥ -2
4. y ≤ 3
5. y ≥ -18/7
6. y > 1