WEBVTT 00:00:00.000 --> 00:00:01.230 00:00:01.230 --> 00:00:04.280 Karibu kwenye kipindi cha milinganyo hatua ya nne. 00:00:04.280 --> 00:00:06.540 Hebu tufanye baadhi ya maswali. 00:00:06.540 --> 00:00:06.710 Hivyo. 00:00:06.710 --> 00:00:09.580 Tuchukulie nina-- ngoja nikupe baadhi ya 00:00:09.580 --> 00:00:20.110 maswali-- kama nikisema 3 juu ya x ni sawa na 5. 00:00:20.110 --> 00:00:23.180 Hivyo, tunachotaka kufanya--hili swali ni tofauti na 00:00:23.180 --> 00:00:24.260 yale tulioyaona. 00:00:24.260 --> 00:00:26.950 Kwa sababu hapa, badala ya kuwa na x kwenye kiasi, tuna 00:00:26.950 --> 00:00:28.150 x kwenye asili. 00:00:28.150 --> 00:00:31.270 Hivyo, sihitaji kuwa na x kwenye asili, 00:00:31.270 --> 00:00:34.190 tunahitaji kuitoa kwenye asili na kuwa kwenye 00:00:34.190 --> 00:00:36.140 kiasi na sio kwenye asili 00:00:36.140 --> 00:00:36.920 kama ifuatavyo. 00:00:36.920 --> 00:00:40.780 Hivyo, njia mojawapo ya kuondoa namba kwenye asili ni hivi, kama 00:00:40.780 --> 00:00:45.560 tunazidisha pande zote za huu mlinganyo kwa x, unaona 00:00:45.560 --> 00:00:47.460 kwenye huu upande wa kushoto wa mlinganyo hizi 00:00:47.460 --> 00:00:48.900 x mbili zitaisha. 00:00:48.900 --> 00:00:52.160 Na upande wa kulia, utapata 5 mara x. 00:00:52.160 --> 00:00:56.920 Hivyo hii ni sawa na -- x mbili zinaisha. 00:00:56.920 --> 00:01:00.890 na unapata 3 ni sawa na 5x. 00:01:00.890 --> 00:01:05.420 Tunaweza kuiandika hivi, 5x ni sawa na 3. 00:01:05.420 --> 00:01:07.810 Kisha tunachagua njia ya kufanya kati ya hizi mbili. 00:01:07.810 --> 00:01:12.210 Tunaweza kuzidisha pande zote kwa 1/5, au unaweza 00:01:12.210 --> 00:01:14.230 kugawanya kwa 5. 00:01:14.230 --> 00:01:16.490 Kama ukizidisha pande zote kwa 1/5. 00:01:16.490 --> 00:01:18.680 Upande wa kushoto unabakia na x. 00:01:18.680 --> 00:01:23.740 Na upande wa kulia ni, 3 mara 1/5, ni sawa na 3/5. 00:01:23.740 --> 00:01:24.640 Nini tulichokifanya hapa? 00:01:24.640 --> 00:01:26.860 Hii inaturudisha kwenye swali la hatua 00:01:26.860 --> 00:01:28.670 ya pili, au swali la hatua ya kwanza, 00:01:28.670 --> 00:01:29.480 napitia kwa haraka. 00:01:29.480 --> 00:01:31.990 Tulichokifanya nikuzidisha pande zote za huu 00:01:31.990 --> 00:01:33.260 mlinganyo kwa x. 00:01:33.260 --> 00:01:35.460 Na tukaitoa x kwenye asili. 00:01:35.460 --> 00:01:36.360 Hebu tufanye swali lingine. 00:01:36.360 --> 00:01:41.110 00:01:41.110 --> 00:01:53.530 Tuchukulie tuna, x jumlisha 2 juu ya x jumlisha 1 ni 00:01:53.530 --> 00:01:58.800 sawa na 7. 00:01:58.800 --> 00:02:00.790 Hapa, badala ya kuwa na x kwenye asili, 00:02:00.790 --> 00:02:02.920 tuna x jumlisha 1 kwenye asili. 00:02:02.920 --> 00:02:05.000 Lakini tutafanya kwa njia ileile. 00:02:05.000 --> 00:02:09.170 Ili kuondoa x jumlisha 1 kwenye asili, tunazidisha pande 00:02:09.170 --> 00:02:15.450 zote za huu mlinganyo mara x jumlisha 1 juu ya 1 mara huu upande. 00:02:15.450 --> 00:02:17.010 Kwa kuwa tumefanya hivyo upande wa kushoto pia tuna 00:02:17.010 --> 00:02:19.640 fanya hivyo upande wa kulia, na hii ni 7/1, 00:02:19.640 --> 00:02:24.420 mara x jumlisha 1 juu ya 1. 00:02:24.420 --> 00:02:27.720 Kwenye upande wa kushoto, x jumlisha 1 zinaisha. 00:02:27.720 --> 00:02:31.110 Na unabakiwa na x jumlisha 2. 00:02:31.110 --> 00:02:33.300 Juu ya 1, lakini tunaiacha 1. 00:02:33.300 --> 00:02:39.260 Hii ni sawa na 7 mara x jumlisha 1. 00:02:39.260 --> 00:02:41.930 Hiyo ni sawa na x jumlisha 2. 00:02:41.930 --> 00:02:45.720 Kumbuka, 7 mara kitu kizima, x jumlisha 1. 00:02:45.720 --> 00:02:47.790 Hivyo tunatakiwa tufungua mabano. 00:02:47.790 --> 00:02:54.400 Na hii ni sawa na 7x jumlisha 7. 00:02:54.400 --> 00:02:57.200 Hii inaturudisha kwenye mlinganyo 00:02:57.200 --> 00:02:58.790 hatua ya tatu. 00:02:58.790 --> 00:03:02.050 Tunachokifanya sasa, tunaweka x zote 00:03:02.050 --> 00:03:02.965 upande mmoja wa mlinganyo. 00:03:02.965 --> 00:03:05.570 Kisha tunaweka namba kamili, ambazo ni 2 na 7, kwenye 00:03:05.570 --> 00:03:07.100 upande mwingine wa mlinganyo 00:03:07.100 --> 00:03:08.890 Hivyo naamua kuweka x upande wa kushoto. 00:03:08.890 --> 00:03:10.990 Hivyo tunaileta 7x kwenye upande wa kushoto. 00:03:10.990 --> 00:03:14.450 Na tunafanya hivyo kwa kutoa 7x pande zote. 00:03:14.450 --> 00:03:19.440 Toa 7x, toa 7x. 00:03:19.440 --> 00:03:22.800 Upande wa kulia, hizi 7x mbili zinaisha. 00:03:22.800 --> 00:03:26.410 Na upande wa kushoto tuna hasi 7x jumlisha x. 00:03:26.410 --> 00:03:32.840 Vizuri, hii ni hasi 6x jumlisha 2 ni sawa na, 00:03:32.840 --> 00:03:35.080 kulia tumebakiwa na 7. 00:03:35.080 --> 00:03:36.470 Hivyo tunataka kuondoa hii 2. 00:03:36.470 --> 00:03:41.360 Na tunfanya hivyo kwa kutoa 2 pande zote. 00:03:41.360 --> 00:03:48.000 Na tutabakiwa na hasi 6x ni sawa na 5. 00:03:48.000 --> 00:03:49.220 Hili ni swali la kwenye hatua ya kwanza. 00:03:49.220 --> 00:03:52.410 Tunatakiwa tuzidishe pande zote mara kinyume katika kuzidisha 00:03:52.410 --> 00:03:54.200 kizidishi upande wa kushoto. 00:03:54.200 --> 00:03:56.150 Na kizidishi ni hasi 6. 00:03:56.150 --> 00:03:59.620 Hivyo tunazidisha pande zote za mlinganyo kwa hasi 1/6. 00:03:59.620 --> 00:04:02.540 00:04:02.540 --> 00:04:05.610 Hasi 1/6. 00:04:05.610 --> 00:04:08.890 Upande wa kushoto, hasi 1 juu ya 6 mara hasi 6. 00:04:08.890 --> 00:04:10.190 Ni sawa na 1, 00:04:10.190 --> 00:04:16.130 Tumepata x ni sawa na 5 mara hasi 1/6. 00:04:16.130 --> 00:04:19.250 Hii ni hasi 5/6. 00:04:19.250 --> 00:04:22.270 00:04:22.270 --> 00:04:23.210 Na tumemaliza. 00:04:23.210 --> 00:04:25.710 Na kama unataka kuhakikisha, utachukua hii x 00:04:25.710 --> 00:04:28.950 sawa na hasi 5/6 na kuiweka kwenye swali letu la awali 00:04:28.950 --> 00:04:30.580 kuthibitisha jibu. 00:04:30.580 --> 00:04:31.340 Tufanye swali lingine. 00:04:31.340 --> 00:04:34.610 00:04:34.610 --> 00:04:37.940 Naandika kwa hapa juu. 00:04:37.940 --> 00:04:40.020 Tuchukulie. 00:04:40.020 --> 00:04:51.010 3 mara x jumlisha 5 ni sawa na 8 mara x jumlisha 2. 00:04:51.010 --> 00:04:52.740 Tunafanya kitu kilekile hapa. 00:04:52.740 --> 00:04:55.950 Ingawa tuna milinganyo miwili, tunayohitaji kuiondoa 00:04:55.950 --> 00:04:56.680 kwenye asili. 00:04:56.680 --> 00:04:58.870 Tunataka kuondoa x jumlisha 5 pia tunataka kuondoa 00:04:58.870 --> 00:05:00.010 x jumlisha 2. 00:05:00.010 --> 00:05:01.670 Tuondoe x jumlisha 5 kwanza. 00:05:01.670 --> 00:05:03.640 Vizuri, kama tulivyofanya awali, tunazidisha pande zote 00:05:03.640 --> 00:05:05.570 za huu mlinganyo kwa x jumlisha 5. 00:05:05.570 --> 00:05:07.630 Unaweza kusema x jumlisha 5 juu ya 1. 00:05:07.630 --> 00:05:12.680 Mara x jumlisha 5 juu ya 1. 00:05:12.680 --> 00:05:15.080 Upande wa kushoto, zinaisha. 00:05:15.080 --> 00:05:24.230 Hivyo tunabakiwa na 3 ni sawa na 8 mara x jumlisha tano. 00:05:24.230 --> 00:05:28.770 juu ya x jumlisha 2. 00:05:28.770 --> 00:05:31.820 Sasa, tunarahisisha, kwa mara nyingine 00:05:31.820 --> 00:05:34.420 tunazidisha 8 mara mlinganyo wote. 00:05:34.420 --> 00:05:41.860 Hivyo ni 8x jumlisha 40 juu ya x jumlisha 2. 00:05:41.860 --> 00:05:43.500 Sasa, tunataka kuondoa x jumlisha 2. 00:05:43.500 --> 00:05:44.510 Hivyo tutafanya njia ileile. 00:05:44.510 --> 00:05:46.505 Tunazidisha pande zote za mlinganyo kwa 00:05:46.505 --> 00:05:50.904 x jumlisha 2 juu ya 1. 00:05:50.904 --> 00:05:52.580 x jumlisha 2. 00:05:52.580 --> 00:05:53.690 Tunaweza kusema tunazidisha 00:05:53.690 --> 00:05:54.420 pande zote kwa x jumlisha 2. 00:05:54.420 --> 00:05:56.630 Hii 1 ni sio ya lazima. 00:05:56.630 --> 00:06:02.910 Hivyo upande wa kushoto unakuwa 3x jumlisha 6. 00:06:02.910 --> 00:06:05.070 Kumbuka kuzidisha mara 3 kote, kwa sababu 00:06:05.070 --> 00:06:07.030 unaizidisha kwa mlinganyo wote. 00:06:07.030 --> 00:06:08.540 x jumlisha 2. 00:06:08.540 --> 00:06:09.860 Kwenye upande wa kulia. 00:06:09.860 --> 00:06:13.620 Hii x jumlisha 2 na hii x jumlisha 2 zinaisha. 00:06:13.620 --> 00:06:16.380 Tunabakiwa na 8x jumlisha 40. 00:06:16.380 --> 00:06:19.340 Na hii ni swali la hatua ya tatu. 00:06:19.340 --> 00:06:25.380 Kama tunatoa 8x pande zote, hasi 8x, jumlisha 00:06:25.380 --> 00:06:26.970 nafikiri nimemaliza nafasi. 00:06:26.970 --> 00:06:28.470 Toa 8x. 00:06:28.470 --> 00:06:31.290 Kwenye upande wa kulia 8x zinaisha. 00:06:31.290 --> 00:06:38.620 Kwenye upande wa kushoto tuna hasi 5x jumlisha 6 ni sawa 00:06:38.620 --> 00:06:42.320 na, kwenye upande wa kulia tumebakiwa na 40. 00:06:42.320 --> 00:06:45.380 Sasa tunatoa 6 kwenye pande zote za mlinganyo. 00:06:45.380 --> 00:06:46.380 Naandika hapa. 00:06:46.380 --> 00:06:49.510 Toa 6 jumlisha toa 6. 00:06:49.510 --> 00:06:51.470 Natumaini mmenielewa 00:06:51.470 --> 00:06:53.160 mpaka hapa. 00:06:53.160 --> 00:06:55.720 00:06:55.720 --> 00:06:58.410 Tukitoa kwa hasi 6 pande zote, upande wa kushoto 00:06:58.410 --> 00:07:05.280 tumebakiwa na hasi 5x sawa na kwenye 00:07:05.280 --> 00:07:08.780 upande wa kulia tuna 34. 00:07:08.780 --> 00:07:09.880 Hili ni swali la kwenye hatua ya kwanza. 00:07:09.880 --> 00:07:12.780 Tunazidisha pande zote mara hasi 1/5. 00:07:12.780 --> 00:07:16.510 00:07:16.510 --> 00:07:18.360 Hasi 1/5. 00:07:18.360 --> 00:07:21.130 Kwenye upande wa kushoto tuna x. 00:07:21.130 --> 00:07:27.130 Na kwenye upande wa kulia tuna hasi 34/5. 00:07:27.130 --> 00:07:29.640 Huenda kuna makosa madogomadogo, lakini natumai nipo sahihi. 00:07:29.640 --> 00:07:33.190 Natumai kama umeelewa tulichofanya hapa, basi 00:07:33.190 --> 00:07:36.780 upo tayari kufanya maswali ya milinganyo ya hatua ya nne. 00:07:36.780 --> 00:07:38.290 Uwe na furaha. 00:07:38.290 --> 00:07:38.790