0:00:00.000,0:00:01.230


0:00:01.230,0:00:04.280
Karibu kwenye kipindi cha milinganyo hatua ya nne.

0:00:04.280,0:00:06.540
Hebu tufanye baadhi ya maswali.

0:00:06.540,0:00:06.710
Hivyo.

0:00:06.710,0:00:09.580
Tuchukulie nina-- ngoja nikupe baadhi ya

0:00:09.580,0:00:20.110
maswali-- kama nikisema 3 juu ya x ni sawa na 5.

0:00:20.110,0:00:23.180
Hivyo, tunachotaka kufanya--hili swali ni tofauti na

0:00:23.180,0:00:24.260
yale tulioyaona.

0:00:24.260,0:00:26.950
Kwa sababu hapa, badala ya kuwa na x kwenye kiasi, tuna

0:00:26.950,0:00:28.150
x kwenye asili.

0:00:28.150,0:00:31.270
Hivyo, sihitaji kuwa na x kwenye asili,

0:00:31.270,0:00:34.190
tunahitaji kuitoa kwenye asili na kuwa kwenye

0:00:34.190,0:00:36.140
kiasi na sio kwenye asili

0:00:36.140,0:00:36.920
kama ifuatavyo.

0:00:36.920,0:00:40.780
Hivyo, njia mojawapo ya kuondoa namba kwenye asili ni hivi, kama

0:00:40.780,0:00:45.560
tunazidisha pande zote za huu mlinganyo kwa x, unaona

0:00:45.560,0:00:47.460
kwenye huu upande wa kushoto wa mlinganyo hizi

0:00:47.460,0:00:48.900
x mbili zitaisha.

0:00:48.900,0:00:52.160
Na upande wa kulia, utapata 5 mara x.

0:00:52.160,0:00:56.920
Hivyo hii ni sawa na -- x mbili zinaisha.

0:00:56.920,0:01:00.890
na unapata 3 ni sawa na 5x.

0:01:00.890,0:01:05.420
Tunaweza kuiandika hivi, 5x ni sawa na 3.

0:01:05.420,0:01:07.810
Kisha tunachagua njia ya kufanya kati ya hizi mbili.

0:01:07.810,0:01:12.210
Tunaweza kuzidisha pande zote kwa 1/5, au unaweza

0:01:12.210,0:01:14.230
kugawanya kwa 5.

0:01:14.230,0:01:16.490
Kama ukizidisha pande zote kwa 1/5.

0:01:16.490,0:01:18.680
Upande wa kushoto unabakia na x.

0:01:18.680,0:01:23.740
Na upande wa kulia ni, 3 mara 1/5, ni sawa na 3/5.

0:01:23.740,0:01:24.640
Nini tulichokifanya hapa?

0:01:24.640,0:01:26.860
Hii inaturudisha kwenye swali la hatua

0:01:26.860,0:01:28.670
ya pili, au swali la hatua ya kwanza,

0:01:28.670,0:01:29.480
napitia kwa haraka.

0:01:29.480,0:01:31.990
Tulichokifanya nikuzidisha pande zote za huu

0:01:31.990,0:01:33.260
mlinganyo kwa x.

0:01:33.260,0:01:35.460
Na tukaitoa x kwenye asili.

0:01:35.460,0:01:36.360
Hebu tufanye swali lingine.

0:01:36.360,0:01:41.110


0:01:41.110,0:01:53.530
Tuchukulie tuna, x jumlisha 2 juu ya x jumlisha 1 ni

0:01:53.530,0:01:58.800
sawa na 7.

0:01:58.800,0:02:00.790
Hapa, badala ya kuwa na x kwenye asili,

0:02:00.790,0:02:02.920
tuna x jumlisha 1 kwenye asili.

0:02:02.920,0:02:05.000
Lakini tutafanya kwa njia ileile.

0:02:05.000,0:02:09.170
Ili kuondoa x jumlisha 1 kwenye asili, tunazidisha pande

0:02:09.170,0:02:15.450
zote za huu mlinganyo mara x jumlisha 1 juu ya 1 mara huu upande.

0:02:15.450,0:02:17.010
Kwa kuwa tumefanya hivyo upande wa kushoto pia tuna

0:02:17.010,0:02:19.640
fanya hivyo upande wa kulia, na hii ni 7/1,

0:02:19.640,0:02:24.420
mara x jumlisha 1 juu ya 1.

0:02:24.420,0:02:27.720
Kwenye upande wa kushoto, x jumlisha 1 zinaisha.

0:02:27.720,0:02:31.110
Na unabakiwa na x jumlisha 2.

0:02:31.110,0:02:33.300
Juu ya 1, lakini tunaiacha 1.

0:02:33.300,0:02:39.260
Hii ni sawa na 7 mara x jumlisha 1.

0:02:39.260,0:02:41.930
Hiyo ni sawa na x jumlisha 2.

0:02:41.930,0:02:45.720
Kumbuka, 7 mara kitu kizima, x jumlisha 1.

0:02:45.720,0:02:47.790
Hivyo tunatakiwa tufungua mabano.

0:02:47.790,0:02:54.400
Na hii ni sawa na 7x jumlisha 7.

0:02:54.400,0:02:57.200
Hii inaturudisha kwenye mlinganyo

0:02:57.200,0:02:58.790
hatua ya tatu.

0:02:58.790,0:03:02.050
Tunachokifanya sasa, tunaweka x zote

0:03:02.050,0:03:02.965
upande mmoja wa mlinganyo.

0:03:02.965,0:03:05.570
Kisha tunaweka namba kamili, ambazo ni 2 na 7, kwenye

0:03:05.570,0:03:07.100
upande mwingine wa mlinganyo

0:03:07.100,0:03:08.890
Hivyo naamua kuweka x upande wa kushoto.

0:03:08.890,0:03:10.990
Hivyo tunaileta 7x kwenye upande wa kushoto.

0:03:10.990,0:03:14.450
Na tunafanya hivyo kwa kutoa 7x pande zote.

0:03:14.450,0:03:19.440
Toa 7x, toa 7x.

0:03:19.440,0:03:22.800
Upande wa kulia, hizi 7x mbili zinaisha.

0:03:22.800,0:03:26.410
Na upande wa kushoto tuna hasi 7x jumlisha x.

0:03:26.410,0:03:32.840
Vizuri, hii ni hasi 6x jumlisha 2 ni sawa na,

0:03:32.840,0:03:35.080
kulia tumebakiwa na 7.

0:03:35.080,0:03:36.470
Hivyo tunataka kuondoa hii 2.

0:03:36.470,0:03:41.360
Na tunfanya hivyo kwa kutoa 2 pande zote.

0:03:41.360,0:03:48.000
Na tutabakiwa na hasi 6x ni sawa na 5.

0:03:48.000,0:03:49.220
Hili ni swali la kwenye hatua ya kwanza.

0:03:49.220,0:03:52.410
Tunatakiwa tuzidishe pande zote mara kinyume katika kuzidisha

0:03:52.410,0:03:54.200
kizidishi upande wa kushoto.

0:03:54.200,0:03:56.150
Na kizidishi ni hasi 6.

0:03:56.150,0:03:59.620
Hivyo tunazidisha pande zote za mlinganyo kwa hasi 1/6.

0:03:59.620,0:04:02.540


0:04:02.540,0:04:05.610
Hasi 1/6.

0:04:05.610,0:04:08.890
Upande wa kushoto, hasi 1 juu ya 6 mara hasi 6.

0:04:08.890,0:04:10.190
Ni sawa na 1,

0:04:10.190,0:04:16.130
Tumepata x ni sawa na 5 mara hasi 1/6.

0:04:16.130,0:04:19.250
Hii ni hasi 5/6.

0:04:19.250,0:04:22.270


0:04:22.270,0:04:23.210
Na tumemaliza.

0:04:23.210,0:04:25.710
Na kama unataka kuhakikisha, utachukua hii x

0:04:25.710,0:04:28.950
sawa na hasi 5/6 na kuiweka kwenye swali letu la awali

0:04:28.950,0:04:30.580
kuthibitisha jibu.

0:04:30.580,0:04:31.340
Tufanye swali lingine.

0:04:31.340,0:04:34.610


0:04:34.610,0:04:37.940
Naandika kwa hapa juu.

0:04:37.940,0:04:40.020
Tuchukulie.

0:04:40.020,0:04:51.010
3 mara x jumlisha 5 ni sawa na 8 mara x jumlisha 2.

0:04:51.010,0:04:52.740
Tunafanya kitu kilekile hapa.

0:04:52.740,0:04:55.950
Ingawa tuna milinganyo miwili, tunayohitaji kuiondoa

0:04:55.950,0:04:56.680
kwenye asili.

0:04:56.680,0:04:58.870
Tunataka kuondoa x jumlisha 5 pia tunataka kuondoa

0:04:58.870,0:05:00.010
x jumlisha 2.

0:05:00.010,0:05:01.670
Tuondoe x jumlisha 5 kwanza.

0:05:01.670,0:05:03.640
Vizuri, kama tulivyofanya awali, tunazidisha pande zote

0:05:03.640,0:05:05.570
za huu mlinganyo kwa x jumlisha 5.

0:05:05.570,0:05:07.630
Unaweza kusema x jumlisha 5 juu ya 1.

0:05:07.630,0:05:12.680
Mara x jumlisha 5 juu ya 1.

0:05:12.680,0:05:15.080
Upande wa kushoto, zinaisha.

0:05:15.080,0:05:24.230
Hivyo tunabakiwa na 3 ni sawa na 8 mara x jumlisha tano.

0:05:24.230,0:05:28.770
juu ya x jumlisha 2.

0:05:28.770,0:05:31.820
Sasa, tunarahisisha, kwa mara nyingine

0:05:31.820,0:05:34.420
tunazidisha 8 mara mlinganyo wote.

0:05:34.420,0:05:41.860
Hivyo ni 8x jumlisha 40 juu ya x jumlisha 2.

0:05:41.860,0:05:43.500
Sasa, tunataka kuondoa x jumlisha 2.

0:05:43.500,0:05:44.510
Hivyo tutafanya njia ileile.

0:05:44.510,0:05:46.505
Tunazidisha pande zote za mlinganyo kwa

0:05:46.505,0:05:50.904
x jumlisha 2 juu ya 1.

0:05:50.904,0:05:52.580
x jumlisha 2.

0:05:52.580,0:05:53.690
Tunaweza kusema tunazidisha

0:05:53.690,0:05:54.420
pande zote kwa x jumlisha 2.

0:05:54.420,0:05:56.630
Hii 1 ni sio ya lazima.

0:05:56.630,0:06:02.910
Hivyo upande wa kushoto unakuwa 3x jumlisha 6.

0:06:02.910,0:06:05.070
Kumbuka kuzidisha mara 3 kote, kwa sababu

0:06:05.070,0:06:07.030
unaizidisha kwa mlinganyo wote.

0:06:07.030,0:06:08.540
x jumlisha 2.

0:06:08.540,0:06:09.860
Kwenye upande wa kulia.

0:06:09.860,0:06:13.620
Hii x jumlisha 2 na hii x jumlisha 2 zinaisha.

0:06:13.620,0:06:16.380
Tunabakiwa na 8x jumlisha 40.

0:06:16.380,0:06:19.340
Na hii ni swali la hatua ya tatu.

0:06:19.340,0:06:25.380
Kama tunatoa 8x pande zote, hasi 8x, jumlisha

0:06:25.380,0:06:26.970
nafikiri nimemaliza nafasi.

0:06:26.970,0:06:28.470
Toa 8x.

0:06:28.470,0:06:31.290
Kwenye upande wa kulia 8x zinaisha.

0:06:31.290,0:06:38.620
Kwenye upande wa kushoto tuna hasi 5x jumlisha 6 ni sawa

0:06:38.620,0:06:42.320
na, kwenye upande wa kulia tumebakiwa na 40.

0:06:42.320,0:06:45.380
Sasa tunatoa 6 kwenye pande zote za mlinganyo.

0:06:45.380,0:06:46.380
Naandika hapa.

0:06:46.380,0:06:49.510
Toa 6 jumlisha toa 6.

0:06:49.510,0:06:51.470
Natumaini mmenielewa

0:06:51.470,0:06:53.160
mpaka hapa.

0:06:53.160,0:06:55.720


0:06:55.720,0:06:58.410
Tukitoa kwa hasi 6 pande zote, upande wa kushoto

0:06:58.410,0:07:05.280
tumebakiwa na hasi 5x sawa na kwenye

0:07:05.280,0:07:08.780
upande wa kulia tuna 34.

0:07:08.780,0:07:09.880
Hili ni swali la kwenye hatua ya kwanza.

0:07:09.880,0:07:12.780
Tunazidisha pande zote mara hasi 1/5.

0:07:12.780,0:07:16.510


0:07:16.510,0:07:18.360
Hasi 1/5.

0:07:18.360,0:07:21.130
Kwenye upande wa kushoto tuna x.

0:07:21.130,0:07:27.130
Na kwenye upande wa kulia tuna hasi 34/5.

0:07:27.130,0:07:29.640
Huenda kuna makosa madogomadogo, lakini natumai nipo sahihi.

0:07:29.640,0:07:33.190
Natumai kama umeelewa tulichofanya hapa, basi

0:07:33.190,0:07:36.780
upo tayari kufanya maswali ya milinganyo ya hatua ya nne.

0:07:36.780,0:07:38.290
Uwe na furaha.

0:07:38.290,0:07:38.790