ALGEBRA, solve these equations?

I'll do the first one. You do the others.

7(x-2)=(5x+1)/2

Get rid of the parnetheses:

7x-14=(5x+1)/2

Get rid of the fraction:

14x-28=5x+1

Group:

9x=29

Solve for x:

x = 29/9

7x - 14 = 5x/2 + 1/2
4.5x = 14.5
x = 29/9 or 3.222

6x + 2 = 4x -28
2x = -30
x = -15

5- 2x/3 = 4
2x/3 = 1
x = 3/2

1.
7(x-2)=(5x+1)/2
7x - 14 = 5/2x + 1/2
4.5x = 14.5
x = 3.22222...etc

2.
6x + 2 = 4(x - 7)
6x + 2 = 4x - 28
2x + 30 = 0
2x = -30
x = -15

3.
(15-2x)/3 = 4
5 - 2/3x = 4
1 - 2/3x = 0
1 = 2/3x
3 = 2x
x = 3/2

The final squaring is beside the point. the only way (...)^2 would properly be 0 is for (...) to be 0. so sparkling up 5z^2 + 6z + 12 = 0 The quadratic formula z = (-b + or - sqrt(b^2 - 4ac))/2a with a = 5, b = 6, c = 12 will supply a destructive cost for b^2 - 4ac, meaning you get complicated roots. Do it your self, yet i think of you get z = -0.6 + 0.2*sqrt(fifty one)*i or z = -0.6 - 0.2*sqrt(fifty one)*i

7(x-2)=(5x+1)/2
(7x-14)*2 = 5x + 1
14x - 5x = 28 + 1
x = 29/9 = 3.22

Check it:
7(3.22-2) =7*1.22=8.54
(5*3.22+1)/2 = 8.55 - ignore rounding error

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6x+2=4(x-7)

6x+2 = 4x-28
2x = 30
x = 15

Check it:
6*15+2=32
4*(15-7)=32 - correct

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(15-2x)/3 =4

15-2x=12
x=3/2=1.5

Check it:

(15-2*1.5)/3
12/4=4 - Correct

14x - 28 = 5x + 1
9x = 29
x = 29/9

6x + 2 = 4x - 28
2x = - 30
x = - 15

15 - 2x = 12
3 = 2x
x = 3/2

1)

Multiply everything by 2 to get rid of the fraction

14(x - 2) = 5x + 1

Multiply out the bracket:

14x - 28 = 5x + 1

Take 5x from both sides:

9x - 28 = 1

Add 28 to both sides:

9x = 29

Divide through by 9:

x = 29/9


2)

Multiply out the bracket:

6x + 2 = 4x - 28

Take 4x from both sides:

2x + 2 = -28

Take 2 from both sides:

2x = -30

Divide through by 2:

x = -15

3)

Multiply through by 3 to get rid of the fraction:

15 - 2x = 12

Take 15 from both sides:

-2x = -3

Divide through by -2

x = -3/-2

Negative divided by a negative is a positive:

x = 3/2


Hope this helps

1)
7(x - 2) = (5x + 1)/2
2(7)(x - 2) = 5x + 1
14(x - 2) = 5x + 1
14(x) - 14(2) = 5x + 1
14x - 28 = 5x + 1
14x - 5x = 28 + 1
9x = 29
x = 29/9

2)
6x + 2 = 4(x - 7)
6x + 2 = 4(x) - 4(7)
6x + 2 = 4x - 28
6x - 4x = -2 - 28
2x = -30
x = -30/2
x = -15

3)
(15 - 2x)/3 = 4
15 - 2x = 3(4)
15 - 2x = 12
2x = 15 - 12
x = 3/2 (1.5)

7(x-2)=(5x+1)/2
7x-14=(5x+1)/2
2(7x-14) = 5x+1
14x-28=5x+1
9x=29
x=29/9
x= approx 3.22

6x+2=4(x-7)
6x+2=4x-28
2x+2=-28
2x=-30
x=-15

(15-2x)/3=4
15-2x=12
3-2x=0
3=2x
3/2=x

2[7(x-2)] = 2[(5x+1)/2]
2(7x-14) = 5x+1
14x-28 = 5x+1
9x = 29
x = 29/9

6x+2 = 4x-28
2x = -30
x = -15

3[(15-2x)/3] = 3(4)
15-2x = 12
-2x = -3
x = 3/2