Soving for x. Could somebody help explain these math problems to me?

10 - (3x + 5)/6 = 47/12 + (x/2)/4

create a common denominator:

120/12 - 2(3x + 5)/12 = 47/12 + 3(x/2)/12

eliminate the denominators:

120 - 2(3x + 5) = 47 + 3(x/2)

subtract 47, add 2(3x + 5) to each side:

73 = 2(3x + 5) + 3(x/2) =

distribute:

73 = 6x + 10 + 3x/2

subtract 10 from both sides:

63 = 6x + 3x/2

create common denominator on right:

63 = 12x/2 + 3x/2

add:

63 = 15x/2

multiply both sides by 2:

126 = 15x

divide both sides by 15:

x = 126/5

3x/8 - 7/10 - (12x - 5)/16 - (2x - 3)/20 + (4x + 9)/4 + 7/80 = 0

put into common denominator:

30x/80 - 56/80 - 5(12x - 5)/80 - 4(2x - 3)/80 + 20(4x + 9)/80 + 7/80 = 0

eliminate the denominators:

30x - 56 - 5(12x - 5) - 4(2x - 3) + 20(4x + 9) + 7 = 0

distribute:

30x - 56 - 60x + 25 - 8x + 12 + 80x + 180 + 7 = 0

collect terms:

42x + 168 = 0

subtract 168 from both sides:

42x = -168

divide both sides by 42:

x = -168/42 = -4

5 + x/4 = (1/3)((2 - x)/2) - 2/3 + (1/4)((10 - 5x)/3) [ I hope that I've copied this as intended}

multiply on the right:

5 + x/4 = (2 - x)/6 - 2/3 + (10 - 5x)/12

put into common denominator:

60/12 + 3x/12 = 2(2 - x)/12 - 8/12 + (10 - 5x)/12

eliminate the denominators:

60 + 3x = 2(2 - x) - 8 + 10 - 5x

distribute on the right:

60 + 3x = 4 - 2x - 8 + 10 - 5x

collect terms:

60 + 3x = 6 - 7x

add 7x, subtract 6 on both sides:

54 + 10x = 0

subtract 54 from both sides:

10x = -54

divide both sides by 10:

x = -54/10

- .--

Thus:

or, (60-18x +5)/6 = 47/12 - x/8

or, (55-18x)/6 = (94 - 3x)/24

or, 55-18x = (94-3x)/4

or, 220 - 72x = 94- 3x

or, 126 = 69x

or, x= 1.8 26

or, 3x/8 -10x - 5/16 +9/4 +7/80 =0

or, 3x/8 -10x +( 7 + 180 -25)/80=0

or, 3x/8 -10x +162/80=0

or,(3x-80x)/8 +162/80 =0

or,1/8 [-77x + 162/10] =0

or, -77x = -16.2

or, x= .210

5+ x/4 = 1/6 -x/6 -2/3 +1/40 -5x/12

or,10x/12 =657/120

or,10x = 657/10

or, x=6.57

or,

10-3x+5/6=47/12-x^2/4 multiply 12 both side

120-36x+10=47-2x^2/4

36x-2x^2/4=83

3x/8-7/10-12x-5/16-2x-3/20+4x+9/4+7/80=0

multiply by 80

30x-56-960x-25-160x-12+320x+180+7=0

770x=94

x=94/770=47/385

5+x/4=1/3(2-x/2)-2/3+1/4(10-5x/3)

20+x=(16-4x)/6-8/3 + (30-5x)/3

120+x=16-4x-16+60-10x

15x=-60

x=-60/15=-4