Equation solve karne ka matlab kya hai?

Iska matlab hai letter-number ki wo value dhoondhna jisse left hand side aur right hand side barabar ho jaayein. 2n + 1 = 99 ke liye wo value 49 hai, kyunki 2 × 49 + 1 = 99. Yahi value equation ka solution hai.

Equation mein dono taraf ek hi kaam kyun karte hain?

Kyunki dono taraf pehle se barabar hain. Dono mein ek hi sankhya jodne, ghataane, guna karne ya bhaag dene se do nayi values milti hain jo ab bhi barabar hain, bilkul waise jaise balanced taraazu dono palde mein barabar wazan jodne ya hataane pe seedha rehta hai.

Kya term ko doosri taraf le jaana aur dono taraf ek hi step karna ek hi baat hai?

Haan. 2y + 7 = 21 ko 2y = 21 − 7 likhna dono taraf se 7 ghataane ka chhota tareeka hai, aur 2y = 14 ko y = 14 ÷ 2 likhna dono taraf 2 se bhaag dene ka chhota tareeka hai. Dono tareekon se jawab ek hi aata hai.

Equations kaise solve karein?

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Equation kya hai?

Equation ek kathan hai ki do expressions barabar hain, jaise 2n + 1 = 99 ya 2z + 4 = 5z − 14. Barabar ke nishaan se pehle wala hissa left hand side (LHS) hai aur baad wala right hand side (RHS). Akshar kisi anjaan sankhya ki jagah hai. Equation solve karna matlab akshar ki wo value dhoondhna jisse LHS aur RHS barabar ho jaayein; wahi value solution hai.

Equation 2n + 1 = 99 ke LHS, RHS, letter-number aur barabar ka nishaan — Equation ke hisse

Trial and error

Ek tareeka hai values aazmaana. 2n + 1 = 99 mein n = 5 se sirf 11 aata hai aur n = 30 se 61. n = 40 se 81 aata hai, thoda paas, aur n = 50 se 101, bas zara zyaada. Phir n = 49 se theek 99 aata hai. Koi aur value kaam nahi karegi, kyunki n ek badhne pe LHS 2 badhta hai. Yahan andaaza chal gaya, par 5x − 4 = 7 ka jawab poori sankhya bhi nahi hai, isliye hamein aisa tareeka chahiye jo hamesha chale.

2n + 1 mein n = 5, 10, 30, 40, 50 aur 49 aazmaakar 99 tak pahunchna — Trial and error

Balance banaaye rakho

Palde waale taraazu ke baare mein socho. Agar dono palde mein barabar wazan hai, to har palde se ek jitna wazan hataane ya jodne pe bhi taraazu seedha rehta hai. Equation bhi aise hi chalti hai. 15 + 8 = 23 se shuru karo: dono taraf 10 jodo to 33 = 33; dono taraf 2 se guna karo to 46 = 46. Ek taraf jo bhi karo, doosri taraf bhi wahi karo, to equation sahi rahegi. (Bas zero se bhaag dena mana hai.)

15 + 8 = 23 ke dono taraf ek hi sankhya jodne, ghataane, guna ya bhaag dene se dono taraf barabar rehte hain — Dono taraf ek hi step

Step by step solve karna

Plan ye hai ki unknown ek taraf akela bache. 5x − 4 = 7 mein − 4 raaste mein hai, to dono taraf 4 jodo: 5x = 11. Ab factor 5 raaste mein hai, to dono taraf 5 se bhaag do: x = 11/5, yaani 2.2. Pehle jod aur ghataana ulto, phir guna aur bhaag.

5x − 4 = 7 solve karna: dono taraf 4 jodo, phir dono taraf 5 se bhaag do, phir check karo — 5x − 4 = 7 solve karna

Hamesha check karo. x = 2.2 waapas rakho: 5 × 2.2 − 4 = 11 − 4 = 7, jo RHS hai, to jawab sahi hai. Isi tarah 11y + (−5) = 61 se 11y = 66 aur y = 6 aata hai, aur 6 × 11 − 5 = 61 isko pakka karta hai.

Dono taraf unknown

6y + 7 = 4y + 21 mein unknown dono taraf hai. Pehle dono taraf se 4y ghataao: 2y + 7 = 21. Phir 7 ghataao: 2y = 14. Phir 2 se bhaag do: y = 7. Bracket pehle kholte hain: 4(m + 6) − 8 = 2m − 4 ban jaata hai 4m + 16 = 2m − 4, to 2m = −20 aur m = −10.

6y + 7 = 4y + 21 ko do tareekon se solve karna: dono taraf ek hi step, aur term ko doosri taraf le jaana — Solve karne ke do tareeke

Jaldi waala tareeka: term ko doosri taraf le jaana

Dekho har step kya karta hai. 2y + 7 = 21 ke dono taraf se 7 ghataane se left ka + 7 gayab ho jaata hai aur right pe − 7 ban kar aa jaata hai: 2y = 21 − 7. To ye step hum seedha likh sakte hain. Isse teen niyam milte hain:

Jo term judi ya ghati ho, wo doosri taraf ulte sign ke saath jaati hai (uska additive inverse).
Jo factor ek taraf guna kar raha ho, wo doosri taraf bhaag ban jaata hai: 2y = 14 se y = 14 ÷ 2.
Jo divisor ho, wo doosri taraf guna ban jaata hai: u ÷ 15 = 6 se u = 6 × 15 = 90.

Equation mein term ko doosri taraf le jaane ke teen niyam, udaaharan ke saath — Term ko doosri taraf le jaana

Mind the Mistake

Zyaadatar galtiyan inse hoti hain: term doosri taraf le jaana par uska sign na badalna, kisi taraf ki sirf ek term ko bhaag dena, ulta bhaag dena (8z = 2 se z = 2/8 aata hai, 4 nahi), aur bracket mein sign ki chook: −2(3 − 4x) hota hai −6 + 8x. Kisi equation ka koi solution na ho, ye bhi ho sakta hai: x + 4 = x + 5 kabhi sahi nahi ho sakti.

Equation solve karne ki chaar aam galtiyan, har ek ka sahi tareeka — Mind the mistake

Ye kyun zaroori hai

Ye kuch steps chapter ki har equation hal kar dete hain, aur aage ki bhi bahut si. Inhe kahaniyon pe lagao word problems se equation kaise banayein mein, aur dekho Bharatiya ganitagyon ne equations kaise solve ki bijaganita: pracheen Bharat mein algebra mein. Textbook ke sawaalon ke jawab Part 2 Chapter 7 ke NCERT solutions mein hain; poore Part 2 Chapter 7 ke notes dekho.