Ukubaluleka Kokulinganisela Ezilinganisweni
Kumathematika, igama elithi "equation" lizwakala lilula: uphawu olulinganayo (=) olubonisa ukuthi izinombolo ezimbili zinenani elifanayo. Kodwa-ke, ngemuva kwalolo phawu kukhona umqondo omkhulu osekela indlela esicabanga ngayo ngokunengqondo, sixazulule izinkinga, futhi senze izinqumo ezisekelwe kudatha. Lowo mqondo omkhulu ibhalansi. Ibhalansi kuma-equation akuyona nje umthetho wobuchwepheshe wokuhambisa izinombolo ukusuka kwesobunxele kuya kwesokudla; kuyisimiso esibalulekile esiqinisekisa ukuthi isinyathelo ngasinye sokubala sihlala silungile futhi siphendula.
Isilinganiso “njengesisindo” semiqondo yenani
Indlela elula yokuqonda i-equation ukucabanga ngesikali esinezingalo ezimbili. Uhlangothi lwesobunxele luphethe isisindo, kanti uhlangothi lwesokudla luphethe esinye isisindo. Uma isikali silinganisiwe, ubuningi ezinhlangothini zombili buyalingana. Ngokufanayo, nge-equation, izinhlangothi zesobunxele nesokudla zinamanani alinganayo.
Isibonelo, kulesi sibalo:
x + 3 = 10
Uhlangothi lwesobunxele "luqukethe" u-x kanye no-3, kanti uhlangothi lwesokudla luqukethe u-10. Uma nje i-equation iyiqiniso, izinhlangothi zombili kumele zilinganise. Umsebenzi wethu ukuthola inani lika-x elenza lelo bhalansi lenzeke. Ngokwemvelo, uma uhlangothi lwesobunxele lukhuliswa ngo-3, khona-ke ukuze lulinganisele ku-10, u-x kumele abe ngu-7. Lokhu kuyingqikithi yokuxazulula i-equation: ukuthola izimo ezigcina ibhalansi.
Kungani Ukulinganisela Kubalulekile?
Ibhalansi ibalulekile ngoba ama-equation ayizitatimende zeqiniso lezibalo. Uma ibhalansi iphukile, isitatimende siba ngamanga. Empeleni, "ukuphula ibhalansi" kwenzeka lapho senza umsebenzi ohlangothini olulodwa kuphela.
Isibonelo esilula:
x + 3 = 10
Uma sisusa u-3 kuphela ohlangothini lwesobunxele:
x = i-10
Lokhu kusobala ukuthi akulungile, ngoba sishintsha inani lohlangothi lwesobunxele kodwa sishiya uhlangothi lwesokudla lungashintshiwe. Ukuze kulondolozwe ibhalansi, umsebenzi kumele wenziwe kuzo zombili izinhlangothi ngendlela efanayo:
Susa u-3 kuzo zombili izinhlangothi:
x + 3 − 3 = 10 − 3
x = i-7
Lesi simiso singase sibonakale singabalulekile, kodwa empeleni sisebenza "njengomqaphi wobuqotho" bokucabanga ngezibalo. Sisiqeqesha ukuba sibe ngabangaguquguquki, abalungile ezenzweni zethu, futhi sigweme ukukhetha imisebenzi ezuzisa uhlangothi olulodwa kuphela.
Imisebenzi Egcina Ibhalansi
Kunemisebenzi eminingana eyisisekelo okuthi, uma yenziwa kuzo zombili izinhlangothi zesibalo, igcine ibhalansi yayo:
1. Engeza inombolo efanayo kuzo zombili izinhlangothi
Uma u-a = b , khona-ke u-a + c = b + c .
2. Susa izinombolo ezifanayo ezinhlangothini zombili
Uma u-a = b , khona-ke u-a − c = b − c .
3. Phindaphinda izinhlangothi zombili ngenombolo efanayo (ngaphandle kuka-zero ezimweni ezithile)
Uma u-a = b , khona-ke u-a·c = b·c .
4. Hlukanisa izinhlangothi zombili ngenombolo efanayo (akunakuba yi-zero)
Uma u-a = b no-c ≠ 0 , khona-ke u-a/c = b/c .
Isibonelo sesicelo:
2x 16
Ukuze ulinganisele, hlukanisa izinhlangothi zombili ngo-2:
2x/2 = 16/2
x = i-8
Ukulingana kusebenza futhi lapho izibalo ziba nzima kakhulu, isibonelo:
3x − 5 = 2x + 7
Ukuze silinganisele, singasusa u-2x kuzo zombili izinhlangothi:
3x − 2x − 5 = 2x − 2x + 7
x - 5 = 7
Bese wengeza u-5 ezinhlangothini zombili:
x - 5 + 5 = 7 + 5
x = i-12
Umphumela wokugcina ulungile ngoba kuzo zonke izigaba, sigcina izinhlangothi zombili zilingana.
Ibhalansi namaphutha avamile
Amaphutha amaningi ekuxazululeni ama-equation ayenzeka ngoba isimiso sokulingana asinakwa noma sisetshenziswa ngenhliziyo engaphelele. Ezinye izibonelo ezivamile:
1. Ukushintsha amagama ngaphandle kokushintsha izimpawu ngendlela efanele
Kuvame ukuzwakala ukuthi "izingxenye ezihambayo zisho ukushintsha izimpawu." Eqinisweni, okwenzekayo ukuthi senza umsebenzi ofanayo kuzo zombili izinhlangothi, hhayi ukudluliselwa okumangalisayo. Isibonelo, kusukela
x + 5 = 12
iba ngu-x = 12 − 5
kufana nokususa u-5 kuzo zombili izinhlangothi. Uma abantu bengaqondi ibhalansi, bangashintsha izimpawu ngendlela engafanele noma benze izinyathelo ezingaguquki.
2. Ukuhlukanisa nge-variable ngaphandle kokuqinisekisa ukuthi inani alilona u-zero
Kweminye i-equation, ukuhlukanisa ngesisho esingaba yi-zero kungasusa izixazululo noma kufake izixazululo ezingamanga. Isibonelo, uma kukhona isici (x - 2), kumelwe siqaphele ngoba u-x angaba ngu-2. Ukulingana akukhona nje "ukwenza into efanayo," kodwa futhi nokuqinisekisa ukusebenza okusebenzayo.
3. Ukususa izimpande noma izikwele ngaphandle kokuqinisekisa
Isibonelo, kuma-equation ahilela izikwele, singathola izixazululo ezidinga ukuhlolwa kabusha ngoba ukusebenza kokugoba izinhlangothi zombili kungandisa amanani angaba khona.
La maphutha abonisa ukuthi ibhalansi akuyona nje inqubo, kodwa iyindlela yokugcina iqiniso.
Ukulingana Njengesisekelo se-Algebra neSayensi
Ama-equation ayilimi lwe-algebra, i-physics, i-chemistry, i-economics, kanye ne-engineering. Ukulingana aqukethe ngokuvamile kumelela izenzakalo zangempela:
– Ku-physics, i-equation yamandla (isb., i-equilibrium) ikhombisa ukuthi amandla aphumayo ayi-zero. I-equilibrium yezibalo ibonakalisa i-equilibrium yomzimba.
– Kumakhemikhali, i-reaction equation kumele ibe nenani elilinganayo lama-athomu ohlangothini lwesobunxele nolwesokudla. Leyo yindlela engokoqobo yokulinganisela.
– Kwezomnotho, izibalo zingachaza ibhalansi phakathi kokufunwa kanye nokuhlinzekwa, noma ubudlelwano phakathi kwezindleko kanye nemali engenayo.
Uma sigcina ibhalansi ezibalweni zezibalo, empeleni sisebenzisa indlela efanayo yokucabanga esetshenziswa ukuqonda izinhlelo zangempela: lonke ushintsho lunomphumela, futhi kumele "lukhokhelwe" ngoshintsho olulinganayo ukuze imodeli ihlale isebenza.
Kusukela kuzibalo kuya ekucabangeni okubucayi
Inzuzo enkulu yokuqonda ukulingana kuma-equation akukhona nje kuphela ikhono lokuxazulula imibuzo yezivivinyo, kodwa futhi namakhono okucabanga ngokujulile. Ukulingana kusiqeqesha ukuthi:
- Gcina ukuvumelana isinyathelo ngesinyathelo.
– Gwema “izinqamuleli” ezonakalisa iqiniso.
- Qinisekisa ukuthi yonke inguquko inesizathu esizwakalayo.
– Hlola kabusha umphumela wokugcina ngokufaka okunye esikhundleni salokho ukuze ufakazele ukuthi isibalo sihlala silinganisiwe.
Isibonelo, ngemva kokuthola u-x = 12 kusuka ku-equation 3x − 5 = 2x + 7 , singahlola:
Kwesobunxele: 3(12) − 5 = 36 − 5 = 31
Kwesokudla: 2(12) + 7 = 24 + 7 = 31
Zombili ziyafana: i-equation iyiqiniso, ibhalansi iyagcinwa.
I-Penutup
Ibhalansi kuma-equation iyisisekelo sezibalo njengesayensi ehlelekile nethembekile. Ifundisa ukuthi uphawu lokulingana aluyona into ehlukanisa "isinyathelo" kanye "nempendulo," kodwa kunalokho luwuphawu lokulingana okumele luhlonishwe. Lapho sixazulula ama-equation, empeleni sigcina "isikali seqiniso" esingaguquki ngamaphutha okusebenza noma izinkolelo ezingafanele.
Ngokuqonda nokusebenzisa isimiso sokulinganisela, asigcini nje ngokuba nekhono elithe xaxa ku-algebra, kodwa futhi siqonde kakhulu ekucabangeni kwethu. Ukulinganisela kwenza izibalo zibe amathuluzi anamandla—hhayi nje izimpawu encwadini, kodwa futhi kube izisekelo zokuqonda umhlaba ngokusebenzisa ingqondo, ukulinganisa, kanye nobudlelwano obunengqondo.
