Question

1)2(3x+1)-x≦3(x+4)2)7x+4(x-2)>6(1+3x)3)2(x-1)-3(x+2)<6(1+x)4)7(y+3)-2(y+2)≧2(5y+1)5)6(3+5y)-(2+7y)≤5(4+3y)6)4(3y-1)-3(y-1)>2(3+y)

Answer 1

1)х$\leq$5

Answer 2

1) Solving the inequality 2(3x+1)-x≦3(x+4):

Let's simplify the inequality step by step:

2(3x+1) - x ≤ 3(x+4)

6x + 2 - x ≤ 3x + 12

Combining like terms:

5x + 2 ≤ 3x + 12

Subtracting 3x from both sides:

5x - 3x + 2 ≤ 12

2x + 2 ≤ 12

Subtracting 2 from both sides:

2x ≤ 10

Dividing both sides by 2:

x ≤ 5

Therefore, the solution to the inequality is x ≤ 5.

2) Solving the inequality 7x+4(x-2) > 6(1+3x):

Let's simplify the inequality step by step:

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

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

Combining like terms:

11x - 8 > 6 + 18x

Subtracting 11x from both sides:

11x - 11x - 8 > 6 + 18x - 11x

-8 > 6 + 7x

Subtracting 6 from both sides:

-8 - 6 > 6 + 7x - 6

-14 > 7x

Dividing both sides by 7 (note that we divide by a negative number, so we need to reverse the inequality sign):

-14/7 < x

Simplifying:

-2 < x

Therefore, the solution to the inequality is x > -2.

3) Solving the inequality 2(x-1)-3(x+2) < 6(1+x):

Let's simplify the inequality step by step:

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

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

Combining like terms:

-1x - 8 < 6 + 6x

Adding 1x to both sides:

-1x - 1x - 8 < 6 + 6x - 1x

-2x - 8 < 6 + 5x

Subtracting 5x from both sides:

-2x - 5x - 8 < 6 + 5x - 5x

-7x - 8 < 6

Adding 8 to both sides:

-7x - 8 + 8 < 6 + 8

-7x < 14

Dividing both sides by -7 (note that we divide by a negative number, so we need to reverse the inequality sign):

x > -2

Therefore, the solution to the inequality is x > -2.

4) Solving the inequality 7(y+3)-2(y+2) ≥ 2(5y+1):

Let's simplify the inequality step by step:

7(y+3) - 2(y+2) ≥ 2(5y+1)

7y + 21 - 2y - 4 ≥ 10y + 2

Combining like terms:

5y + 17 ≥ 10y + 2

Subtracting 5y from both sides:

5y - 5y + 17 ≥ 10y - 5y + 2

17 ≥ 5y + 2

Subtracting 2 from both sides:

17 - 2 ≥ 5y + 2 - 2

15 ≥ 5y

Dividing both sides by 5:

3 ≥ y

Therefore, the solution to the inequality is y ≤ 3.

5) Solving the inequality 6(3+5y)-(2+7y) ≤ 5(4+3y):

Let's simplify the inequality step by step:

6(3+5y) - (2+7y) ≤ 5(4+3y)

18 + 30y - 2 - 7y ≤ 20 + 15y

Combining like terms:

28 + 23y ≤ 20 + 15y

Subtracting 15y from both sides:

28 + 23y - 15y ≤ 20 + 15y - 15y

28 + 8y ≤ 20

Subtracting 28 from both sides:

28 - 28 + 8y ≤ 20 - 28

8y ≤ -8

Dividing both sides by 8:

y ≤ -1

Therefore, the solution to the inequality is y ≤ -1.

6) Solving the inequality 4(3y-1) - 3(y-1) > 2(3+y):

Let's simplify the inequality step by step:

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

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

Combining like terms:

9y - 1 > 6 + 2y

Subtracting 2y from both sides:

9y - 2y - 1 > 6 + 2y - 2y

7y - 1 > 6

Adding 1 to both sides:

7y - 1 + 1 > 6 + 1

7y > 7

Dividing both sides by 7:

y > 1

Therefore, the solution to the inequality is y > 1.

To summarize the solutions to the inequalities:

1) x ≤ 5 2) x > -2 3) x > -2 4) y ≤ 3 5) y ≤ -1 6) y > 1