1
00:00:01,023 --> 00:00:04,028
欢迎观看线性方程第四课

2
00:00:04,028 --> 00:00:06,053
现在让我们来在一些题目吧

3
00:00:06,054 --> 00:00:06,070
好

4
00:00:06,071 --> 00:00:09,058
现在来看一个比较不一样的问题

5
00:00:09,058 --> 00:00:20,010
如果说我有 X 分之 3 等于 5

6
00:00:20,010 --> 00:00:23,017
那我们该怎么下手呢?

7
00:00:23,017 --> 00:00:24,025
这跟我们平常看到的有点不一样

8
00:00:24,026 --> 00:00:26,094
因为 X 并不是分子

9
00:00:26,094 --> 00:00:28,012
而是在分母里面

10
00:00:28,014 --> 00:00:31,026
因为我自己是不喜欢看到 X 在分母

11
00:00:31,026 --> 00:00:34,017
所以我们得把这 X

12
00:00:34,017 --> 00:00:36,013
赶快从分母移出来

13
00:00:36,014 --> 00:00:36,092
于到分子里面去

14
00:00:36,092 --> 00:00:40,077
那, 我们就得在等号的两边

15
00:00:40,078 --> 00:00:45,056
都乘以 X

16
00:00:45,056 --> 00:00:47,045
你看左边的除 X 乘 X

17
00:00:47,046 --> 00:00:48,089
就会互抵消掉

18
00:00:48,089 --> 00:00:52,014
然后在右边呢, 就会剩下 5 乘以 X

19
00:00:52,014 --> 00:00:56,090
这算一算, 两个 X 互取消掉

20
00:00:56,092 --> 00:01:00,088
你就剩下 3= 5X

21
00:01:00,089 --> 00:01:05,042
当然这也可以被写成 5X = 3

22
00:01:05,042 --> 00:01:07,081
之后我们可以从两个方向着手

23
00:01:07,081 --> 00:01:12,020
我们可以在两边都乘以 1/5

24
00:01:12,020 --> 00:01:14,021
或者是两边都除以 5

25
00:01:14,023 --> 00:01:16,048
如果你两边都乘以 1/5 的话

26
00:01:16,048 --> 00:01:18,067
左边就剩下一个 X

27
00:01:18,068 --> 00:01:23,073
右边呢, 3 乘以 1/5, 就是 3/5

28
00:01:23,073 --> 00:01:24,062
好, 我们刚刚其实是做了甚么呢?

29
00:01:24,064 --> 00:01:26,084
其实你看, 我们已经把

30
00:01:26,084 --> 00:01:28,065
一个进阶的问题

31
00:01:28,067 --> 00:01:29,048
在瞬变成一个基本的题目了

32
00:01:29,048 --> 00:01:31,098
我们只在两边都

33
00:01:31,098 --> 00:01:33,025
再乘以 X

34
00:01:33,026 --> 00:01:35,045
就简单地将 X 从分母里移出来

35
00:01:35,045 --> 00:01:36,034
现在再来试试看别得题目吧

36
00:01:41,009 --> 00:01:53,051
我说, 这里有(X+2)/(X+1)

37
00:01:53,053 --> 00:01:58,079
等于 7 好了

38
00:01:58,079 --> 00:02:00,078
你看, 这里不单有 X 在份母里

39
00:02:00,079 --> 00:02:02,090
我们还有一个 X 在分子里面

40
00:02:02,092 --> 00:02:04,098
可是我们也是用一样的做法

41
00:02:05,000 --> 00:02:09,015
要将 X 加 1 从分母调出来

42
00:02:09,015 --> 00:02:15,043
我们就得两边都乘以 X+1

43
00:02:15,043 --> 00:02:17,000
因为我们在左边先乘了

44
00:02:17,000 --> 00:02:19,062
就要在右边也做一样的

45
00:02:19,062 --> 00:02:24,040
也就是 7/1 乘以(X+1)/1

46
00:02:24,040 --> 00:02:27,071
在左边, 两个 X + 1 会取消掉

47
00:02:27,071 --> 00:02:31,009
剩下 X + 2

48
00:02:31,011 --> 00:02:33,028
其实是 (X+2)/1, 可是那可以不用写

49
00:02:33,030 --> 00:02:39,025
然后右边是 7 乘以 (X+1)

50
00:02:39,025 --> 00:02:41,091
这等于左边的 X + 2

51
00:02:41,093 --> 00:02:45,071
要记得, 这 7 乘是乘以整个 X+ 1

52
00:02:45,071 --> 00:02:47,077
所以我们得用分配乘法的原则

53
00:02:47,078 --> 00:02:54,038
两个数字分别乘以 7 = 7X + 7

54
00:02:54,040 --> 00:02:57,018
那这一次程序

55
00:02:57,018 --> 00:02:58,078
又变再进阶一点的了

56
00:02:58,078 --> 00:03:02,003
我们现在就需要

57
00:03:02,005 --> 00:03:02,096
把所有的 X 都归在一边

58
00:03:02,096 --> 00:03:05,056
然后把其余的固定数, 像 2 跟 7

59
00:03:05,056 --> 00:03:07,009
放到另一边去

60
00:03:07,009 --> 00:03:08,087
如果说我选择把 X 于左边

61
00:03:08,087 --> 00:03:10,097
那就得把 7X 移到左边去

62
00:03:10,099 --> 00:03:14,043
记得那就是两边都减掉 7X

63
00:03:14,043 --> 00:03:19,043
左边多了一个 -7X

64
00:03:19,043 --> 00:03:22,078
右边呢? 两个 7X 互相取消掉

65
00:03:22,080 --> 00:03:26,040
左边现在就变成负 7X 加 X 加 2

66
00:03:26,040 --> 00:03:32,083
也就是 -(6X +2)

67
00:03:32,084 --> 00:03:35,008
等于右边剩下的 7

68
00:03:35,008 --> 00:03:36,046
那现在就要把这个 2 也拿掉

69
00:03:36,046 --> 00:03:41,034
先从两边都减去 2

70
00:03:41,036 --> 00:03:47,099
让这里剩下 - 6X = 6

71
00:03:48,000 --> 00:03:49,021
那现在又变回基本题目了

72
00:03:49,021 --> 00:03:52,038
我们只需要两边都乘以

73
00:03:52,040 --> 00:03:54,018
X 以前系数的倒数

74
00:03:54,018 --> 00:03:56,013
系数是 -6

75
00:03:56,015 --> 00:03:59,061
所以两边都得乘以倒数 - 1/6

76
00:04:02,053 --> 00:04:05,059
- 1/6

77
00:04:05,061 --> 00:04:08,087
左边呢, -1/6 乘以 -6

78
00:04:08,087 --> 00:04:10,018
就等于 1

79
00:04:10,018 --> 00:04:16,011
左边的 X 就等于右边的 5 乘以 -1/6

80
00:04:16,012 --> 00:04:19,024
就是 -5/6

81
00:04:22,025 --> 00:04:23,018
就是这样!

82
00:04:23,019 --> 00:04:25,069
如果你想确定一下的话

83
00:04:25,069 --> 00:04:28,093
可是将答案 "-5/6"

84
00:04:28,093 --> 00:04:30,056
套进原来的方程序里算算对不对

85
00:04:30,056 --> 00:04:31,031
再来试一题吧

86
00:04:34,061 --> 00:04:37,093
我现在随便再编一题

87
00:04:37,093 --> 00:04:40,000
抱歉让我想一想

88
00:04:40,000 --> 00:04:51,000
3X + 5 = 8X + 2

89
00:04:51,000 --> 00:04:52,073
还是一样的

90
00:04:52,074 --> 00:04:55,093
虽然现在是有两个表达式

91
00:04:55,093 --> 00:04:56,067
要从分母中抽走

92
00:04:56,068 --> 00:04:58,086
我们得拿走这 X + 5

93
00:04:58,087 --> 00:05:00,000
和这 X + 2

94
00:05:00,000 --> 00:05:01,066
那先来做 X 加 5

95
00:05:01,067 --> 00:05:03,062
跟以前一样, 我们两边

96
00:05:03,062 --> 00:05:05,056
都乘以 X 加 5

97
00:05:05,056 --> 00:05:07,062
这你可以写成 (X +5)/1

98
00:05:07,062 --> 00:05:12,067
就是乘以 (X+5)/1

99
00:05:12,068 --> 00:05:15,006
在左边, 互相取消了

100
00:05:15,006 --> 00:05:24,022
剩下 3 = 8X+5

101
00:05:24,023 --> 00:05:28,075
这全部都有一个 X+2 的共同份母

102
00:05:28,075 --> 00:05:31,081
现在看这上面, 简化一下

103
00:05:31,081 --> 00:05:34,041
我们只需要将整个表达式乘以 8

104
00:05:34,042 --> 00:05:41,085
就是 (8X + 40)/(X+2)

105
00:05:41,086 --> 00:05:43,049
然后就轮到这分母 (X+2)

106
00:05:43,050 --> 00:05:44,050
还是一样的道理

107
00:05:44,050 --> 00:05:46,049
两边都乘以

108
00:05:46,050 --> 00:05:50,088
(X+2)/1

109
00:05:50,089 --> 00:05:52,056
X + 2

110
00:05:52,056 --> 00:05:53,068
我们也可是说成是

111
00:05:53,068 --> 00:05:54,041
两边都乘以 X+2

112
00:05:54,042 --> 00:05:56,062
这一个就不需要了

113
00:05:56,062 --> 00:06:02,089
左边就会变成 3X + 6

114
00:06:02,091 --> 00:06:05,006
要记得, 这个 3 是要被分配到

115
00:06:05,006 --> 00:06:07,000
这个表达式里面每一个数字

116
00:06:07,001 --> 00:06:08,052
X + 2

117
00:06:08,054 --> 00:06:09,085
然后到右边

118
00:06:09,086 --> 00:06:13,061
这两个 X +2 当然就被取消掉了

119
00:06:13,062 --> 00:06:16,037
之后就剩下 8X+40

120
00:06:16,037 --> 00:06:19,031
又是这种进阶题目了

121
00:06:19,032 --> 00:06:25,037
先得从两边都减去 8X

122
00:06:25,037 --> 00:06:26,095
我可能没位置写了

123
00:06:26,097 --> 00:06:28,047
这减 8X

124
00:06:28,047 --> 00:06:31,027
好, 在右边 俩 8X 被取消

125
00:06:31,029 --> 00:06:38,061
在左边有 -5X + 6

126
00:06:38,062 --> 00:06:42,031
等于右边剩下的 40

127
00:06:42,031 --> 00:06:45,037
那现在两边都减去 6

128
00:06:45,037 --> 00:06:46,037
我把它写到这边

129
00:06:46,037 --> 00:06:49,049
- 6 加 -6

130
00:06:49,050 --> 00:06:51,045
我再移到上面一下

131
00:06:51,047 --> 00:06:53,014
希望大家还跟得上

132
00:06:55,072 --> 00:06:58,039
在两边都减去 6 以后

133
00:06:58,041 --> 00:07:05,026
左边就是 -5X

134
00:07:05,026 --> 00:07:08,076
右边就是 36

135
00:07:08,076 --> 00:07:09,087
这又回到基本去了

136
00:07:09,087 --> 00:07:12,075
我们可以两边都乘以-1/5

137
00:07:16,050 --> 00:07:18,035
这是 -1/5

138
00:07:18,036 --> 00:07:21,012
左边变成 X

139
00:07:21,012 --> 00:07:27,012
右边变成-34/5

140
00:07:27,012 --> 00:07:29,062
这应该就是答案了, 除非我不小心弄错了甚么

141
00:07:29,062 --> 00:07:33,018
如果你都看得懂刚刚的解说

142
00:07:33,018 --> 00:07:36,075
那你就是准备好做第四课的一次方程序了

143
00:07:36,076 --> 00:07:38,027
加油!