化簡&解方程式～急～

一、
1.
x - (1/4)(x - 3) - (1/6)(2 - 3x)
= (12x / 12) - [3(x - 3) / 12] - [2(2 - 3x) / 12]
= [12x - 3(x - 3) - 2(2 - 3x)] / 12
= [12x - 3x + 9 - 4 - 6x] / 12
= (3x+ 5) / 12
（所給的答案錯誤。）

2.
(1/2)(x + 3) - (1/5)(x - 6)
= [5(x + 3) / 10] - [2(x - 6) / 10]
= [5(x + 3) - 2(x - 6)] / 10
= [5x + 15 - 2x + 12] / 10
= (3x + 27) / 10

3.
[(7x - 1) / 4] - [(8x - 3) / 6]
= [3(7x - 1) / 12] - [2(8x - 3) / 12]
= [3(7x - 1) - 2(8x - 3)] / 12
= [21x - 3 - 16x + 6] / 12
= (5x + 3) / 12

4.
[(2x - 1) / 5] - [(1 - 6x) / 3]
= [3(2x - 1) / 15] - [5(1 - 6x) / 15]
= [3(2x - 1) - 5(1 - 6x)] / 15
= [6x - 3 - 5 + 30x] / 15
= (36x - 8) / 15


二、
1.
[(x + 2) / 3] + [(3 - 4x) / 6] = -1
[2(x + 2) / 6] + [(3 - 4x) / 6] = -1
[2(x + 2) + (3 - 4x)] / 6 = -1
[2x + 4 + 3 - 4x] / 6 = -1
[-2x + 7] / 6 = -1
-2x + 7 = -6
2x = 13
x = 13/2

2.
[(2x - 1) / 5] - [(1 - 6x) / 3] = 1
[3(2x - 1) / 15] - [5(1 - 6x) / 15] = 1
[3(2x - 1) - 5(1 - 6x)] / 15 = 1
[6x - 3 - 5 + 30x] / 15 = 1
36x - 8 = 15
36x = 23
x = 23/36

3.
(1/15)(x - 3) = (1/5) - (1/20)(x + 6)
(x - 3) / 15 = (4 / 20) - [(x + 6) / 20]
(x - 3) / 15 = [4 - (x + 6)] / 20
(x - 3) / 3 = (4 - x - 6) / 4
(x - 3) / 3 = (-2 - x) / 4
4(x - 3) = 3(-2 - x)
4x - 12 = -6 - 3x
7x = 6
x = 6/7