Question

1)4(x-3)=x+6 ;2) 4-6(x+2)=3-5x ; 3)(5x+8)-(8x=14)=9 ;4)2,7+3y=9(y-2,1) ; 5)0,3(8-3y)=3,2-0,8(y-7) ; 6)5\6(1\3x-1\5)=3x+3 1\3 ;7) 4(x-1)=2(2x-8)+12;8) 7(4x-1)=6-2(3-14x) Даю 35 баллов

Answer 1

1)4 (x-3)=x+6

4x-12=x+6

4x-x=6+12

3x=18

x=6

2)4-6 (x+2)=3-5x

4-6x-12=3-5x

-8-6x=3-5x

-6x+5x=3+8

-x=11

x=-11

3)(5x+8)-(8x-14)=9

5x+8-8x+14=9

-3x+6=9

-3x=9-6

-3x=3

x=1

4)2,7+3y=9 (y-2,1)

2,7+3y=9y-18,9

3y-9y=-18,9-2,7

-6y=-21,6

y=3,6

5)0,3 (8-3y)=3,2-0,8 (y-7)

2,4 -0,9y=3,2-0,8y+5,6

2,4-0,9y=8,8-0,8y

-0,9y+0,8y=8,8-2,4

-0,1y=6,4

y=-64

6)5\6 (1\3x-1\5)=3x+3

5\18x-1\6=3x-3

5x-3=54x-54

5x-54x=-54+3

-49x=-51

x=51\49

x=1 2\49

7)4(x-1)=2 (2x-8)+12

4x-4=4x-16+12

-4=-16+12

-4=-4

x принадлежит множеству R

8)7(4x-1)=6-2 (3-14x)

28x-7=6-6+28x

-7=0

x принадлежит нулевом множеству

Answer 2

To solve each of these equations, I'll simplify and isolate the variable x or y. Let's go through each equation one by one:

1. 4(x-3) = x+6

Expand the left side: 4x - 12 = x + 6

Move all x terms to one side and constant terms to the other: 4x - x = 6 + 12 3x = 18

Now, isolate x: x = 18 / 3 x = 6

2. 4 - 6(x+2) = 3 - 5x

Distribute the -6 on the left side: 4 - 6x - 12 = 3 - 5x

Combine like terms: -6x - 8 = 3 - 5x

Move all x terms to one side and constant terms to the other: -6x + 5x = 3 + 8 -x = 11

Now, isolate x: x = -11

3. (5x + 8) - (8x = 14) = 9

There seems to be a typo here. I assume you meant: (5x + 8) - (8x - 14) = 9

Simplify the expression: 5x + 8 - 8x + 14 = 9

Combine like terms: -3x + 22 = 9

Move all x terms to one side and constant terms to the other: -3x = 9 - 22 -3x = -13

Now, isolate x: x = -13 / -3 x = 13/3 or approximately 4.33

4. 2.7 + 3y = 9(y - 2.1)

Distribute 9 on the right side: 2.7 + 3y = 9y - 18.9

Move all y terms to one side and constant terms to the other: 3y - 9y = -18.9 - 2.7 -6y = -21.6

Now, isolate y: y = -21.6 / -6 y = 3.6

5. 0.3(8 - 3y) = 3.2 - 0.8(y - 7)

Distribute 0.3 and -0.8 on their respective terms: 2.4 - 0.9y = 3.2 - 0.8y + 6.4

Move all y terms to one side and constant terms to the other: -0.9y + 0.8y = 3.2 + 6.4 - 2.4 -0.1y = 7.2

Now, isolate y: y = 7.2 / -0.1 y = -72

6. 5/6(1/3x - 1/5) = 3x + 3 1/3

Distribute 5/6 on the left side: (5/6) * (1/3x) - (5/6) * (1/5) = 3x + 3 1/3

Simplify the left side: (5/18)x - 5/30 = 3x + 10/3

Move all x terms to one side and constant terms to the other: (5/18)x - 3x = 10/3 + 5/30

Common denominator for the fractions is 18: (5/18)x - (54/18)x = (200/30) + (3/30) (-49/18)x = 203/30

Now, isolate x: x = (203/30) / (-49/18) x = (203/30) * (-18/49) x = -7.8

7. 4(x-1) = 2(2x-8) + 12

Expand the expressions: 4x - 4 = 4x - 16 + 12

Combine like terms: 4x - 4 = 4x - 4

Subtract 4x from both sides: -4 = 0

The equation has no solution. There is no value of x that satisfies this equation.

8. 7(4x-1) = 6 - 2(3-14x)

Distribute 7 and -2 on their respective terms: 28x - 7 = 6 - 6 + 28x

Combine like terms: 28x - 7 = 28x

Subtract 28x from both sides: -7 = 0

The equation has no solution. There is no value of x that satisfies this equation.

In conclusion:

1. x = 6
2. x = -11
3. x = 13/3 or approximately 4.33
4. y = 3.6
5. y = -72
6. x = -7.8
7. No solution for x
8. No solution for x

Considering that some equations have no solutions, I have solved all the equations to the best of my ability, and the sum of the awarded points is 35.