1
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2
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Karibu kwenye kipindi cha milinganyo hatua ya nne.

3
00:00:04,280 --> 00:00:06,540
Hebu tufanye baadhi ya maswali.

4
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Hivyo.

5
00:00:06,710 --> 00:00:09,580
Tuchukulie nina-- ngoja nikupe baadhi ya

6
00:00:09,580 --> 00:00:20,110
maswali-- kama nikisema 3 juu ya x ni sawa na 5.

7
00:00:20,110 --> 00:00:23,180
Hivyo, tunachotaka kufanya--hili swali ni tofauti na

8
00:00:23,180 --> 00:00:24,260
yale tulioyaona.

9
00:00:24,260 --> 00:00:26,950
Kwa sababu hapa, badala ya kuwa na x kwenye kiasi, tuna

10
00:00:26,950 --> 00:00:28,150
x kwenye asili.

11
00:00:28,150 --> 00:00:31,270
Hivyo, sihitaji kuwa na x kwenye asili,

12
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tunahitaji kuitoa kwenye asili na kuwa kwenye

13
00:00:34,190 --> 00:00:36,140
kiasi na sio kwenye asili

14
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kama ifuatavyo.

15
00:00:36,920 --> 00:00:40,780
Hivyo, njia mojawapo ya kuondoa namba kwenye asili ni hivi, kama

16
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tunazidisha pande zote za huu mlinganyo kwa x, unaona

17
00:00:45,560 --> 00:00:47,460
kwenye huu upande wa kushoto wa mlinganyo hizi

18
00:00:47,460 --> 00:00:48,900
x mbili zitaisha.

19
00:00:48,900 --> 00:00:52,160
Na upande wa kulia, utapata 5 mara x.

20
00:00:52,160 --> 00:00:56,920
Hivyo hii ni sawa na -- x mbili zinaisha.

21
00:00:56,920 --> 00:01:00,890
na unapata 3 ni sawa na 5x.

22
00:01:00,890 --> 00:01:05,420
Tunaweza kuiandika hivi, 5x ni sawa na 3.

23
00:01:05,420 --> 00:01:07,810
Kisha tunachagua njia ya kufanya kati ya hizi mbili.

24
00:01:07,810 --> 00:01:12,210
Tunaweza kuzidisha pande zote kwa 1/5, au unaweza

25
00:01:12,210 --> 00:01:14,230
kugawanya kwa 5.

26
00:01:14,230 --> 00:01:16,490
Kama ukizidisha pande zote kwa 1/5.

27
00:01:16,490 --> 00:01:18,680
Upande wa kushoto unabakia na x.

28
00:01:18,680 --> 00:01:23,740
Na upande wa kulia ni, 3 mara 1/5, ni sawa na 3/5.

29
00:01:23,740 --> 00:01:24,640
Nini tulichokifanya hapa?

30
00:01:24,640 --> 00:01:26,860
Hii inaturudisha kwenye swali la hatua

31
00:01:26,860 --> 00:01:28,670
ya pili, au swali la hatua ya kwanza,

32
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napitia kwa haraka.

33
00:01:29,480 --> 00:01:31,990
Tulichokifanya nikuzidisha pande zote za huu

34
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mlinganyo kwa x.

35
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Na tukaitoa x kwenye asili.

36
00:01:35,460 --> 00:01:36,360
Hebu tufanye swali lingine.

37
00:01:36,360 --> 00:01:41,110


38
00:01:41,110 --> 00:01:53,530
Tuchukulie tuna, x jumlisha 2 juu ya x jumlisha 1 ni

39
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sawa na 7.

40
00:01:58,800 --> 00:02:00,790
Hapa, badala ya kuwa na x kwenye asili,

41
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tuna x jumlisha 1 kwenye asili.

42
00:02:02,920 --> 00:02:05,000
Lakini tutafanya kwa njia ileile.

43
00:02:05,000 --> 00:02:09,170
Ili kuondoa x jumlisha 1 kwenye asili, tunazidisha pande

44
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zote za huu mlinganyo mara x jumlisha 1 juu ya 1 mara huu upande.

45
00:02:15,450 --> 00:02:17,010
Kwa kuwa tumefanya hivyo upande wa kushoto pia tuna

46
00:02:17,010 --> 00:02:19,640
fanya hivyo upande wa kulia, na hii ni 7/1,

47
00:02:19,640 --> 00:02:24,420
mara x jumlisha 1 juu ya 1.

48
00:02:24,420 --> 00:02:27,720
Kwenye upande wa kushoto, x jumlisha 1 zinaisha.

49
00:02:27,720 --> 00:02:31,110
Na unabakiwa na x jumlisha 2.

50
00:02:31,110 --> 00:02:33,300
Juu ya 1, lakini tunaiacha 1.

51
00:02:33,300 --> 00:02:39,260
Hii ni sawa na 7 mara x jumlisha 1.

52
00:02:39,260 --> 00:02:41,930
Hiyo ni sawa na x jumlisha 2.

53
00:02:41,930 --> 00:02:45,720
Kumbuka, 7 mara kitu kizima, x jumlisha 1.

54
00:02:45,720 --> 00:02:47,790
Hivyo tunatakiwa tufungua mabano.

55
00:02:47,790 --> 00:02:54,400
Na hii ni sawa na 7x jumlisha 7.

56
00:02:54,400 --> 00:02:57,200
Hii inaturudisha kwenye mlinganyo

57
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hatua ya tatu.

58
00:02:58,790 --> 00:03:02,050
Tunachokifanya sasa, tunaweka x zote

59
00:03:02,050 --> 00:03:02,965
upande mmoja wa mlinganyo.

60
00:03:02,965 --> 00:03:05,570
Kisha tunaweka namba kamili, ambazo ni 2 na 7, kwenye

61
00:03:05,570 --> 00:03:07,100
upande mwingine wa mlinganyo

62
00:03:07,100 --> 00:03:08,890
Hivyo naamua kuweka x upande wa kushoto.

63
00:03:08,890 --> 00:03:10,990
Hivyo tunaileta 7x kwenye upande wa kushoto.

64
00:03:10,990 --> 00:03:14,450
Na tunafanya hivyo kwa kutoa 7x pande zote.

65
00:03:14,450 --> 00:03:19,440
Toa 7x, toa 7x.

66
00:03:19,440 --> 00:03:22,800
Upande wa kulia, hizi 7x mbili zinaisha.

67
00:03:22,800 --> 00:03:26,410
Na upande wa kushoto tuna hasi 7x jumlisha x.

68
00:03:26,410 --> 00:03:32,840
Vizuri, hii ni hasi 6x jumlisha 2 ni sawa na,

69
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kulia tumebakiwa na 7.

70
00:03:35,080 --> 00:03:36,470
Hivyo tunataka kuondoa hii 2.

71
00:03:36,470 --> 00:03:41,360
Na tunfanya hivyo kwa kutoa 2 pande zote.

72
00:03:41,360 --> 00:03:48,000
Na tutabakiwa na hasi 6x ni sawa na 5.

73
00:03:48,000 --> 00:03:49,220
Hili ni swali la kwenye hatua ya kwanza.

74
00:03:49,220 --> 00:03:52,410
Tunatakiwa tuzidishe pande zote mara kinyume katika kuzidisha

75
00:03:52,410 --> 00:03:54,200
kizidishi upande wa kushoto.

76
00:03:54,200 --> 00:03:56,150
Na kizidishi ni hasi 6.

77
00:03:56,150 --> 00:03:59,620
Hivyo tunazidisha pande zote za mlinganyo kwa hasi 1/6.

78
00:03:59,620 --> 00:04:02,540


79
00:04:02,540 --> 00:04:05,610
Hasi 1/6.

80
00:04:05,610 --> 00:04:08,890
Upande wa kushoto, hasi 1 juu ya 6 mara hasi 6.

81
00:04:08,890 --> 00:04:10,190
Ni sawa na 1,

82
00:04:10,190 --> 00:04:16,130
Tumepata x ni sawa na 5 mara hasi 1/6.

83
00:04:16,130 --> 00:04:19,250
Hii ni hasi 5/6.

84
00:04:19,250 --> 00:04:22,270


85
00:04:22,270 --> 00:04:23,210
Na tumemaliza.

86
00:04:23,210 --> 00:04:25,710
Na kama unataka kuhakikisha, utachukua hii x

87
00:04:25,710 --> 00:04:28,950
sawa na hasi 5/6 na kuiweka kwenye swali letu la awali

88
00:04:28,950 --> 00:04:30,580
kuthibitisha jibu.

89
00:04:30,580 --> 00:04:31,340
Tufanye swali lingine.

90
00:04:31,340 --> 00:04:34,610


91
00:04:34,610 --> 00:04:37,940
Naandika kwa hapa juu.

92
00:04:37,940 --> 00:04:40,020
Tuchukulie.

93
00:04:40,020 --> 00:04:51,010
3 mara x jumlisha 5 ni sawa na 8 mara x jumlisha 2.

94
00:04:51,010 --> 00:04:52,740
Tunafanya kitu kilekile hapa.

95
00:04:52,740 --> 00:04:55,950
Ingawa tuna milinganyo miwili, tunayohitaji kuiondoa

96
00:04:55,950 --> 00:04:56,680
kwenye asili.

97
00:04:56,680 --> 00:04:58,870
Tunataka kuondoa x jumlisha 5 pia tunataka kuondoa

98
00:04:58,870 --> 00:05:00,010
x jumlisha 2.

99
00:05:00,010 --> 00:05:01,670
Tuondoe x jumlisha 5 kwanza.

100
00:05:01,670 --> 00:05:03,640
Vizuri, kama tulivyofanya awali, tunazidisha pande zote

101
00:05:03,640 --> 00:05:05,570
za huu mlinganyo kwa x jumlisha 5.

102
00:05:05,570 --> 00:05:07,630
Unaweza kusema x jumlisha 5 juu ya 1.

103
00:05:07,630 --> 00:05:12,680
Mara x jumlisha 5 juu ya 1.

104
00:05:12,680 --> 00:05:15,080
Upande wa kushoto, zinaisha.

105
00:05:15,080 --> 00:05:24,230
Hivyo tunabakiwa na 3 ni sawa na 8 mara x jumlisha tano.

106
00:05:24,230 --> 00:05:28,770
juu ya x jumlisha 2.

107
00:05:28,770 --> 00:05:31,820
Sasa, tunarahisisha, kwa mara nyingine

108
00:05:31,820 --> 00:05:34,420
tunazidisha 8 mara mlinganyo wote.

109
00:05:34,420 --> 00:05:41,860
Hivyo ni 8x jumlisha 40 juu ya x jumlisha 2.

110
00:05:41,860 --> 00:05:43,500
Sasa, tunataka kuondoa x jumlisha 2.

111
00:05:43,500 --> 00:05:44,510
Hivyo tutafanya njia ileile.

112
00:05:44,510 --> 00:05:46,505
Tunazidisha pande zote za mlinganyo kwa

113
00:05:46,505 --> 00:05:50,904
x jumlisha 2 juu ya 1.

114
00:05:50,904 --> 00:05:52,580
x jumlisha 2.

115
00:05:52,580 --> 00:05:53,690
Tunaweza kusema tunazidisha

116
00:05:53,690 --> 00:05:54,420
pande zote kwa x jumlisha 2.

117
00:05:54,420 --> 00:05:56,630
Hii 1 ni sio ya lazima.

118
00:05:56,630 --> 00:06:02,910
Hivyo upande wa kushoto unakuwa 3x jumlisha 6.

119
00:06:02,910 --> 00:06:05,070
Kumbuka kuzidisha mara 3 kote, kwa sababu

120
00:06:05,070 --> 00:06:07,030
unaizidisha kwa mlinganyo wote.

121
00:06:07,030 --> 00:06:08,540
x jumlisha 2.

122
00:06:08,540 --> 00:06:09,860
Kwenye upande wa kulia.

123
00:06:09,860 --> 00:06:13,620
Hii x jumlisha 2 na hii x jumlisha 2 zinaisha.

124
00:06:13,620 --> 00:06:16,380
Tunabakiwa na 8x jumlisha 40.

125
00:06:16,380 --> 00:06:19,340
Na hii ni swali la hatua ya tatu.

126
00:06:19,340 --> 00:06:25,380
Kama tunatoa 8x pande zote, hasi 8x, jumlisha

127
00:06:25,380 --> 00:06:26,970
nafikiri nimemaliza nafasi.

128
00:06:26,970 --> 00:06:28,470
Toa 8x.

129
00:06:28,470 --> 00:06:31,290
Kwenye upande wa kulia 8x zinaisha.

130
00:06:31,290 --> 00:06:38,620
Kwenye upande wa kushoto tuna hasi 5x jumlisha 6 ni sawa

131
00:06:38,620 --> 00:06:42,320
na, kwenye upande wa kulia tumebakiwa na 40.

132
00:06:42,320 --> 00:06:45,380
Sasa tunatoa 6 kwenye pande zote za mlinganyo.

133
00:06:45,380 --> 00:06:46,380
Naandika hapa.

134
00:06:46,380 --> 00:06:49,510
Toa 6 jumlisha toa 6.

135
00:06:49,510 --> 00:06:51,470
Natumaini mmenielewa

136
00:06:51,470 --> 00:06:53,160
mpaka hapa.

137
00:06:53,160 --> 00:06:55,720


138
00:06:55,720 --> 00:06:58,410
Tukitoa kwa hasi 6 pande zote, upande wa kushoto

139
00:06:58,410 --> 00:07:05,280
tumebakiwa na hasi 5x sawa na kwenye

140
00:07:05,280 --> 00:07:08,780
upande wa kulia tuna 34.

141
00:07:08,780 --> 00:07:09,880
Hili ni swali la kwenye hatua ya kwanza.

142
00:07:09,880 --> 00:07:12,780
Tunazidisha pande zote mara hasi 1/5.

143
00:07:12,780 --> 00:07:16,510


144
00:07:16,510 --> 00:07:18,360
Hasi 1/5.

145
00:07:18,360 --> 00:07:21,130
Kwenye upande wa kushoto tuna x.

146
00:07:21,130 --> 00:07:27,130
Na kwenye upande wa kulia tuna hasi 34/5.

147
00:07:27,130 --> 00:07:29,640
Huenda kuna makosa madogomadogo, lakini natumai nipo sahihi.

148
00:07:29,640 --> 00:07:33,190
Natumai kama umeelewa tulichofanya hapa, basi

149
00:07:33,190 --> 00:07:36,780
upo tayari kufanya maswali ya milinganyo ya hatua ya nne.

150
00:07:36,780 --> 00:07:38,290
Uwe na furaha.

151
00:07:38,290 --> 00:07:38,790