1
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歡迎觀看一次方程第四課

2
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現在讓我們來在一些題目吧

3
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好

4
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現在來看一個比較不一樣的問題

5
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如果說我有 X 分之 3 等於 5

6
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那我們該怎麽下手呢?

7
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這跟我們平常看到的有點不一樣

8
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因爲 X 並不是分子

9
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而是在分母裏面

10
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因爲我自己是不喜歡看到 X 在分母

11
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所以我們得把這 X

12
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趕快從分母移出來

13
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於到分子裏面去

14
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那, 我們就得在等號的兩邊

15
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都乘以 X

16
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你看左邊的除 X 乘 X

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就會互抵消掉

18
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然後在右邊呢, 就會剩下 5 乘以 X

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這算一算, 兩個 X 互取消掉

20
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你就剩下 3= 5X

21
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當然這也可以被寫成 5X = 3

22
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之後我們可以從兩個方向著手

23
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我們可以在兩邊都乘以 1/5

24
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或者是兩邊都除以 5

25
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如果你兩邊都乘以 1/5 的話

26
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左邊就剩下一個 X

27
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右邊呢, 3 乘以 1/5, 就是 3/5

28
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好, 我們剛剛其實是做了甚麽呢?

29
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其實你看, 我們已經把

30
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一個進階的問題

31
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在瞬變成一個基本的題目了

32
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我們只在兩邊都

33
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再乘以 X

34
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就簡單地將 X 從分母裏移出來

35
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現在再來試試看別得題目吧

36
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我說, 這裡有(X+2)/(X+1)

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等於 7 好了

38
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你看, 這裡不單有 X 在份母裏

39
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我們還有一個 X 在分子裏面

40
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可是我們也是用一樣的做法

41
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要將 X 加 1 從分母調出來

42
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我們就得兩邊都乘以 X+1

43
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因爲我們在左邊先乘了

44
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就要在右邊也做一樣的

45
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也就是 7/1 乘以(X+1)/1

46
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在左邊, 兩個 X + 1 會取消掉

47
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剩下 X + 2

48
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其實是 (X+2)/1, 可是那可以不用寫

49
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然後右邊是 7 乘以 (X+1)

50
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這等於左邊的 X + 2

51
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要記得, 這 7 乘是乘以整個 X+ 1

52
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所以我們得用分配乘法的原則

53
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兩個數字分別乘以 7 = 7X + 7

54
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那這一次程序

55
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又變再進階一點的了

56
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我們現在就需要

57
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把所有的 X 都歸在一邊

58
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然後把其余的固定數, 像 2 跟 7

59
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放到另一邊去

60
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如果說我選擇把 X 於左邊

61
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那就得把 7X 移到左邊去

62
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記得那就是兩邊都減掉 7X

63
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左邊多了一個 -7X

64
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右邊呢? 兩個 7X 互相取消掉

65
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左邊現在就變成負 7X 加 X 加 2

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也就是 -(6X +2)

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等於右邊剩下的 7

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那現在就要把這個 2 也拿掉

69
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先從兩邊都減去 2

70
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讓這裡剩下 - 6X = 6

71
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那現在又變回基本題目了

72
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我們只需要兩邊都乘以

73
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X 以前係數的倒數

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係數是 -6

75
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所以兩邊都得乘以倒數 - 1/6

76
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- 1/6

77
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左邊呢, -1/6 乘以 -6

78
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就等於 1

79
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左邊的 X 就等於右邊的 5 乘以 -1/6

80
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就是 -5/6

81
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就是這樣!

82
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如果你想確定一下的話

83
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可是將答案 "-5/6"

84
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套進原來的方程序裏算算對不對

85
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再來試一題吧

86
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我現在隨便再編一題

87
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抱歉讓我想一想

88
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3X + 5 = 8X + 2

89
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還是一樣的

90
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雖然現在是有兩個表達式

91
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要從分母中抽走

92
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我們得拿走這 X + 5

93
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和這 X + 2

94
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那先來做 X 加 5

95
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跟以前一樣, 我們兩邊

96
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都乘以 X 加 5

97
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這你可以寫成 (X +5)/1

98
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就是乘以 (X+5)/1

99
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在左邊, 互相取消了

100
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剩下 3 = 8X+5

101
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這全部都有一個 X+2 的共同份母

102
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現在看這上面, 簡化一下

103
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我們只需要將整個表達式乘以 8

104
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就是 (8X + 40)/(X+2)

105
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然後就輪到這分母 (X+2)

106
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還是一樣的道理

107
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兩邊都乘以

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(X+2)/1

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X + 2

110
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我們也可是說成是

111
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兩邊都乘以 X+2

112
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這一個就不需要了

113
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左邊就會變成 3X + 6

114
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要記得, 這個 3 是要被分配到

115
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這個表達式裏面每一個數字

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X + 2

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然後到右邊

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這兩個 X +2 當然就被取消掉了

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之後就剩下 8X+40

120
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又是這種進階題目了

121
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先得從兩邊都減去 8X

122
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我可能沒位置寫了

123
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這減 8X

124
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好, 在右邊 倆 8X 被取消

125
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在左邊有 -5X + 6

126
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等於右邊剩下的 40

127
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那現在兩邊都減去 6

128
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我把它寫到這邊

129
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- 6 加 -6

130
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我再移到上面一下

131
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希望大家還跟得上

132
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在兩邊都減去 6 以後

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左邊就是 -5X

134
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右邊就是 36

135
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這又回到基本去了

136
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我們可以兩邊都乘以-1/5

137
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這是 -1/5

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左邊變成 X

139
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右邊變成-34/5

140
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這應該就是答案了, 除非我不小心弄錯了甚麽

141
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如果你都看得懂剛剛的解說

142
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那你就是準備好做第四課的一次方程序了

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加油!