Menene ma'auni: ma'anar, bayani, misalai

A cikin wannan ɗaba'ar, za mu dubi menene ma'auni, da kuma abin da ake nufi da warware shi. Bayanin ka'idar da aka gabatar yana tare da misalai masu amfani don kyakkyawar fahimta.

Ma'anar daidaito

Daidaiton shine , yana ƙunshe da lambar da ba a san inda za a samo ba.

Yawanci ana nuna wannan lambar ta ƙaramin haruffan Latin (mafi yawanci - x, y or z) kuma ana kiransa m daidaito.

Ma'ana, daidaito shine ma'auni ne kawai idan ya ƙunshi harafin da kuke son ƙididdige ƙimarsa.

Misalai mafi sauƙi daidaitattun daidaito (aikin ƙididdiga ɗaya wanda ba a san shi ba):

• x +3 = 5
• kuma – 2 = 12
• z + 10 = 41

A cikin hadaddun ma'auni, ma'auni na iya faruwa sau da yawa, kuma suna iya ƙunsar baka da kuma hadaddun ayyuka na lissafi. Misali:

• 2x + 4 - x = 10
• 3 (y - 2) + 4y = 15
• x² +5 = 9

Hakanan, ana iya samun sauye-sauye da yawa a cikin lissafin, misali:

• x + 2y = 14
• (2x - y) 2 + 5z = 22

Tushen lissafin

Bari mu ce muna da ma'auni 2x + 6 = 16.

Yana juya zuwa daidaiton gaskiya lokacin x = 5. Wannan darajar (lamba) ita ce tushen daidaito.

A warware ma'auni - wannan yana nufin gano tushensa ko tushensa (ya danganta da adadin masu canji), ko tabbatar da cewa babu su.

Yawancin lokaci, tushen yana rubuta kamar haka: x = 3. Idan akwai tushen da yawa, ana jera su kawai ta hanyar waƙafi, misali: x₁ = 2, x₂ = -5.

Notes:

1. Wasu ƙila ba za a iya warware su ba.

Misali: 0 · x = 7. Ko wace lamba muka musanya x, ba zai yi aiki don samun daidaito daidai ba. A wannan yanayin, amsar ita ce: "Equation ba shi da tushe."

2. Wasu ma'auni suna da adadin tushen tushe mara iyaka.

Misali: kuma = kuma. A wannan yanayin, mafita ita ce kowace lamba, watau x ∈ R, x ∈Z, x ∈ Nina N, Z и R su ne na halitta, lamba da ainihin lambobi, bi da bi.

Daidaitan Daidaitawa

Ana kiran ma'auni masu tushe iri ɗaya daidai da.

Misali: x +3 = 5 и 2x + 4 = 8. Ga ma'auni guda biyu, mafita ita ce lamba biyu, watau x = 2.

Asalin daidaitattun canje-canje na daidaito:

1. Canja wurin wani lokaci daga wani sashi na daidaitattun zuwa wani tare da canza alamar sa zuwa akasin haka.

Misali: 3x + 7 = 5 daidai da 3x + 7-5 = 0.

2. Yawawa / rarraba sassan biyu na lissafin da lamba ɗaya, ba daidai da sifili ba.

Misali: 4x - 7 = 17 daidai da 8x - 14 = 34.

Ma'auni kuma baya canzawa idan an ƙara/rage lamba ɗaya zuwa ɓangarorin biyu.

3. Rage sharuddan makamancin haka.

Misali: 2x + 5x – 6 + 2 = 14 daidai da 7x - 18 = 0.