[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.04,0:00:04.04,Default,,0000,0000,0000,,Bine ati venit la prezentarea "Rezolvarea Inegalitatilor"
Dialogue: 0,0:00:04.04,0:00:07.00,Default,,0000,0000,0000,,sau lectia se poate numi si inegalitati algebrice (inecuatiii).
Dialogue: 0,0:00:07.00,0:00:09.02,Default,,0000,0000,0000,,Deci, hai sa incepem
Dialogue: 0,0:00:09.03,0:00:12.05,Default,,0000,0000,0000,,Daca am spune ca, eii bine, sa spunem doar ca
Dialogue: 0,0:00:12.05,0:00:17.09,Default,,0000,0000,0000,,x>5 ( x mai mare ca 5) , ok?
Dialogue: 0,0:00:18.00,0:00:22.08,Default,,0000,0000,0000,,Deci x poate fi 5,01, poate fi 5,5 , poate fi un milion.
Dialogue: 0,0:00:22.09,0:00:26.03,Default,,0000,0000,0000,,Nu poate fi 4 sau 3 sau -8
Dialogue: 0,0:00:26.04,0:00:28.01,Default,,0000,0000,0000,,De fapt, doar pentru a ilustra,
Dialogue: 0,0:00:28.02,0:00:31.00,Default,,0000,0000,0000,,sa desenam aceasta pe axa numerelor.
Dialogue: 0,0:00:31.01,0:00:33.03,Default,,0000,0000,0000,,Aceasta este axa numerelor.
Dialogue: 0,0:00:33.03,0:00:36.09,Default,,0000,0000,0000,,Si daca acesta este 5, x nu poate fi egal cu 5
Dialogue: 0,0:00:37.00,0:00:39.09,Default,,0000,0000,0000,,deci vom desena un cerc mare aici si apoi vom colora
Dialogue: 0,0:00:40.00,0:00:42.01,Default,,0000,0000,0000,,toate valorile pe care le poate avea x.
Dialogue: 0,0:00:42.02,0:00:45.08,Default,,0000,0000,0000,,Deci x poate fi 5,000001
Dialogue: 0,0:00:45.09,0:00:48.06,Default,,0000,0000,0000,,poate fi doar un pic mai mare decat 5
Dialogue: 0,0:00:48.07,0:00:50.09,Default,,0000,0000,0000,,si toate aceste valori vor satisface inecuatia, corect?
Dialogue: 0,0:00:51.00,0:00:53.06,Default,,0000,0000,0000,,Deci, haideti sa scriem cateva numere ce satisfac inecuatia.
Dialogue: 0,0:00:53.07,0:00:56.01,Default,,0000,0000,0000,,6 satisface, 10 satisface,
Dialogue: 0,0:00:56.02,0:00:57.09,Default,,0000,0000,0000,,100 va satisface deasemenea.
Dialogue: 0,0:00:58.00,0:01:01.00,Default,,0000,0000,0000,,Acum, daca vom multiplica sau vom imparti
Dialogue: 0,0:01:01.01,0:01:03.08,Default,,0000,0000,0000,,ambii mebrii , cred ca ii putem spune ecuatie,
Dialogue: 0,0:01:03.09,0:01:09.08,Default,,0000,0000,0000,,sau inecuatie, cu -1 , vreau sa intelegem ce se intampla.
Dialogue: 0,0:01:09.09,0:01:15.09,Default,,0000,0000,0000,,Deci care este relatia intre -x si -5?
Dialogue: 0,0:01:17.04,0:01:19.00,Default,,0000,0000,0000,,Si cand spun , care este relatia,
Dialogue: 0,0:01:19.00,0:01:24.03,Default,,0000,0000,0000,,inteleg " -x este mai mare sau mai mic decat -5"?
Dialogue: 0,0:01:24.03,0:01:27.72,Default,,0000,0000,0000,,Ei bine, 6 este valoarea care functioneaza pt x
Dialogue: 0,0:01:27.72,0:01:33.03,Default,,0000,0000,0000,,deci -6 , este mai mare sau mai mic decat -5?
Dialogue: 0,0:01:33.03,0:01:36.09,Default,,0000,0000,0000,,-6 este mai mic decat -5 , corect?
Dialogue: 0,0:01:37.00,0:01:41.01,Default,,0000,0000,0000,,Daca imi permiteti voi desena axa numerelor aici.
Dialogue: 0,0:01:41.01,0:01:44.04,Default,,0000,0000,0000,,Daca avem -5 aici - sa desenam un cerc in jurul lui
Dialogue: 0,0:01:44.05,0:01:46.07,Default,,0000,0000,0000,,deoarece stim ca x nu va fi egal cu -5
Dialogue: 0,0:01:46.08,0:01:48.05,Default,,0000,0000,0000,,deoarece am decis
Dialogue: 0,0:01:48.06,0:01:50.01,Default,,0000,0000,0000,,ca este mai mare sau egall cu el.
Dialogue: 0,0:01:50.02,0:01:54.04,Default,,0000,0000,0000,,deci spunem ca 6 functioneaza pentru x ,deci -6 este aici, corect?
Dialogue: 0,0:01:54.04,0:01:56.04,Default,,0000,0000,0000,,-6
Dialogue: 0,0:01:56.04,0:01:58.61,Default,,0000,0000,0000,,Deci -6 este mai mic decat -5
Dialogue: 0,0:01:58.61,0:02:03.02,Default,,0000,0000,0000,,La fel -10, la fel este -100 , la fel -1.000.000, corect?
Dialogue: 0,0:02:03.02,0:02:08.10,Default,,0000,0000,0000,,Deci daca inmultim cu -1 , -x este mai mic decat -5
Dialogue: 0,0:02:08.10,0:02:11.33,Default,,0000,0000,0000,,Deci aceasta este cu adevarat tot ce trebuie sa va amintiti.
Dialogue: 0,0:02:11.33,0:02:14.44,Default,,0000,0000,0000,,Cand lucrati cu inegalitati in algebra
Dialogue: 0,0:02:14.44,0:02:18.20,Default,,0000,0000,0000,,Inecuatiile le puteti trata in acest mod
Dialogue: 0,0:02:18.20,0:02:21.10,Default,,0000,0000,0000,,A> sau a< , semnul ">" il tratati in acelasi mod cu semnul "="
Dialogue: 0,0:02:21.10,0:02:24.75,Default,,0000,0000,0000,,Singura diferenta este : daca inmultiti sau impartiti
Dialogue: 0,0:02:24.75,0:02:29.82,Default,,0000,0000,0000,,ambii termeni ai inegalitatii cu un numar negativ
Dialogue: 0,0:02:29.82,0:02:30.65,Default,,0000,0000,0000,,se schimba sensul inecuatiei.
Dialogue: 0,0:02:30.65,0:02:31.77,Default,,0000,0000,0000,,Tot ceea ce trebuie sa va amintiti.
Dialogue: 0,0:02:31.78,0:02:34.32,Default,,0000,0000,0000,,haideti sa facem cateva probleme care vor lamuri aceste lucruri.
Dialogue: 0,0:02:34.32,0:02:38.06,Default,,0000,0000,0000,,Daca veti uita vreodata, trebuie doar sa incercati, este suficient sa va amintiti ca
Dialogue: 0,0:02:38.06,0:02:41.28,Default,,0000,0000,0000,,dac x>5 , atunci -x<-5
Dialogue: 0,0:02:41.28,0:02:42.24,Default,,0000,0000,0000,,si incercati si cu alte numere
Dialogue: 0,0:02:42.24,0:02:45.52,Default,,0000,0000,0000,,Aceasta va forma intuitia supra axei numerelor.
Dialogue: 0,0:02:45.52,0:02:46.94,Default,,0000,0000,0000,,Haideti sa facem cateva probleme
Dialogue: 0,0:02:46.94,0:02:56.14,Default,,0000,0000,0000,,deci, daca 3x+2 este mai mic sau egal cu 1
Dialogue: 0,0:02:56.14,0:02:58.08,Default,,0000,0000,0000,,Ei bine, aceasta est o inecuatie destul de usor de rezolvat
Dialogue: 0,0:02:58.08,0:03:01.40,Default,,0000,0000,0000,,Vom spune, haideti sa scadem 2 din ambii termeni
Dialogue: 0,0:03:01.40,0:03:03.10,Default,,0000,0000,0000,,Cand adunam sau scadem
Dialogue: 0,0:03:03.10,0:03:04.88,Default,,0000,0000,0000,,sensul inegalitatii nu se schimba
Dialogue: 0,0:03:04.88,0:03:07.66,Default,,0000,0000,0000,,Deci , daca scadem 2 din ambii termeni
Dialogue: 0,0:03:07.66,0:03:12.45,Default,,0000,0000,0000,,Obtinem 3x mai mic sau egal cu -1 , corect?
Dialogue: 0,0:03:12.45,0:03:16.53,Default,,0000,0000,0000,,Apoi vom imparti ambii termeni la 3
Dialogue: 0,0:03:16.53,0:03:22.29,Default,,0000,0000,0000,,Obtinem x mai mic sau egal cu -1/3
Dialogue: 0,0:03:22.29,0:03:24.01,Default,,0000,0000,0000,,Priviti! Nu s-a schimbat nimic
Dialogue: 0,0:03:24.01,0:03:26.70,Default,,0000,0000,0000,,deoarece am impartit ambii termeni la o valoare pozitiva
Dialogue: 0,0:03:26.70,0:03:31.95,Default,,0000,0000,0000,,Corect? Aceasta inecuatie se putea rezolva intr-o alta forma
Dialogue: 0,0:03:31.95,0:03:35.44,Default,,0000,0000,0000,,Ce ar fi daca scadem 1 din ambii termeni
Dialogue: 0,0:03:35.44,0:03:37.58,Default,,0000,0000,0000,,Deci e o alta forma de rezolvare
Dialogue: 0,0:03:37.58,0:03:42.39,Default,,0000,0000,0000,,Daca spunem ca 3x+1 mai mic sau egal cu 0
Dialogue: 0,0:03:42.39,0:03:44.46,Default,,0000,0000,0000,,Scadem 1 din ambii termeni
Dialogue: 0,0:03:44.46,0:03:46.64,Default,,0000,0000,0000,,si apoi scadem 3x din ambii termeni
Dialogue: 0,0:03:46.64,0:03:51.46,Default,,0000,0000,0000,,obtinem 1 mai mic sau egal cu -3x
Dialogue: 0,0:03:51.46,0:03:53.48,Default,,0000,0000,0000,,Am scazut 3x de aici
Dialogue: 0,0:03:53.48,0:03:54.78,Default,,0000,0000,0000,,Deci voi scadea 3x si de aici
Dialogue: 0,0:03:54.78,0:03:58.26,Default,,0000,0000,0000,,Acum trebuie sa impart ambii termeni la un numar negativ
Dialogue: 0,0:03:58.26,0:04:02.35,Default,,0000,0000,0000,,Corect? Deoarece urmeaza sa impart ambii termeni la -3
Dialogue: 0,0:04:02.35,0:04:05.47,Default,,0000,0000,0000,,voi obtine -1/3 in acest termen
Dialogue: 0,0:04:05.47,0:04:07.25,Default,,0000,0000,0000,,bazat pe ceea ce tocmai am invatat
Dialogue: 0,0:04:07.27,0:04:08.48,Default,,0000,0000,0000,,atunci cand impartim ambii termeni ai unei inecuatii cu un numar negativ
Dialogue: 0,0:04:08.48,0:04:10.26,Default,,0000,0000,0000,,se schimba sensul inegalitatii
Dialogue: 0,0:04:10.26,0:04:11.78,Default,,0000,0000,0000,,Era mai "mic sau egal cu"
Dialogue: 0,0:04:11.78,0:04:15.16,Default,,0000,0000,0000,,iar acum este mai "mare sau egal cu"
Dialogue: 0,0:04:15.16,0:04:19.18,Default,,0000,0000,0000,,Acum, avem acelasi rezultat cand avem doua rezolvari diferite?
Dialogue: 0,0:04:19.18,0:04:22.57,Default,,0000,0000,0000,,dincolo avem x mai mic sau egal cu -1/3
Dialogue: 0,0:04:22.57,0:04:25.92,Default,,0000,0000,0000,,acesta este rezultatul ;-1/3 mai mare sau egal cu x
Dialogue: 0,0:04:25.92,0:04:27.40,Default,,0000,0000,0000,,Este acelasi rezultat, corect?
Dialogue: 0,0:04:27.40,0:04:29.58,Default,,0000,0000,0000,,x mai mic sau egal cu -1/3
Dialogue: 0,0:04:29.58,0:04:31.96,Default,,0000,0000,0000,,Asta este ceea ce mi se pare elegant in algebra.
Dialogue: 0,0:04:31.96,0:04:33.96,Default,,0000,0000,0000,,Poti trata orice problema in mai multe modalitati.
Dialogue: 0,0:04:33.96,0:04:37.56,Default,,0000,0000,0000,,Si vei avea acelasi rezultat atat timp cat procedezi in mod corect.
Dialogue: 0,0:04:37.56,0:04:41.89,Default,,0000,0000,0000,,Haideti sa mai facem cateva probleme.
Dialogue: 0,0:04:41.89,0:04:46.86,Default,,0000,0000,0000,,Voi sterge aici. Asa. haideti sa face un exercitiu ceva mai greu.
Dialogue: 0,0:04:46.86,0:04:56.75,Default,,0000,0000,0000,,Sa spunem ca -8x+7>5x+2
Dialogue: 0,0:04:56.75,0:05:02.14,Default,,0000,0000,0000,,Sa scadem 5x dinn ambii termeni.
Dialogue: 0,0:05:02.14,0:05:06.08,Default,,0000,0000,0000,,-13x+7>2 ( -13x plus7 mai mare decat 2)
Dialogue: 0,0:05:06.08,0:05:09.75,Default,,0000,0000,0000,,Acum vom scadea 7 din ambii termeni,
Dialogue: 0,0:05:09.75,0:05:13.47,Default,,0000,0000,0000,,-13x>-5 (-13x mai mare decat 5)
Dialogue: 0,0:05:13.47,0:05:17.31,Default,,0000,0000,0000,,Acum vom impartii ambii termeni ai inecuatiei la -13.
Dialogue: 0,0:05:17.31,0:05:19.46,Default,,0000,0000,0000,,Ei bine, foarte simplu.
Dialogue: 0,0:05:19.46,0:05:24.94,Default,,0000,0000,0000,,Aici este doar x , iar in celalalt termen -5/-13=5/13, corect?
Dialogue: 0,0:05:24.94,0:05:26.70,Default,,0000,0000,0000,,Semnul negativ se anuleaza.
Dialogue: 0,0:05:26.70,0:05:30.07,Default,,0000,0000,0000,,Si atat timp cat impartim la un numar negativ,
Dialogue: 0,0:05:30.07,0:05:31.85,Default,,0000,0000,0000,,vom schimba semnul inecuatiei.
Dialogue: 0,0:05:31.85,0:05:34.29,Default,,0000,0000,0000,,x mai mic decat 5/13
Dialogue: 0,0:05:34.29,0:05:35.72,Default,,0000,0000,0000,,Inca odata , exact ca la inceput,
Dialogue: 0,0:05:35.72,0:05:37.97,Default,,0000,0000,0000,,daca nu ma credeti incercati cu cateva numere.
Dialogue: 0,0:05:37.97,0:05:39.08,Default,,0000,0000,0000,,Imi amintesc , atunci cand am invatat pentru prima oara acest lucru
Dialogue: 0,0:05:39.08,0:05:40.73,Default,,0000,0000,0000,,nu credeam ce imi spunea profesorul , deci am incercat cateva numere
Dialogue: 0,0:05:40.75,0:05:44.54,Default,,0000,0000,0000,,si asa m-am convins ca este adevarat
Dialogue: 0,0:05:44.54,0:05:47.05,Default,,0000,0000,0000,,cand inmultesti sau imparti termenii unei inegalitati
Dialogue: 0,0:05:47.05,0:05:50.22,Default,,0000,0000,0000,,cu un numar negativ, sensul acesteia se schimba.
Dialogue: 0,0:05:50.22,0:05:53.04,Default,,0000,0000,0000,,Si atentie: aceasta regula este doar pentru inmultire sau impartire
Dialogue: 0,0:05:53.05,0:05:55.78,Default,,0000,0000,0000,,nu cand aduni sau scazi
Dialogue: 0,0:05:55.78,0:05:57.66,Default,,0000,0000,0000,,Cred ca trebuie sa va dau
Dialogue: 0,0:05:57.66,0:05:59.81,Default,,0000,0000,0000,,o idee buna despre cum sa rezolvati aceste probleme
Dialogue: 0,0:05:59.81,0:06:01.08,Default,,0000,0000,0000,,Nu sunt multe lucruri noi aici
Dialogue: 0,0:06:01.08,0:06:05.29,Default,,0000,0000,0000,,Rezolvati o inegalitate sau cred ca se poate numi
Dialogue: 0,0:06:05.29,0:06:08.00,Default,,0000,0000,0000,,inecuatie - veti rezolva-o exact la fel
Dialogue: 0,0:06:08.01,0:06:10.08,Default,,0000,0000,0000,,cum rezolvati o ecuatie normala.
Dialogue: 0,0:06:10.08,0:06:14.48,Default,,0000,0000,0000,,Singura diferenta este atunci cand inmultiti sau impartiti
Dialogue: 0,0:06:14.48,0:06:16.03,Default,,0000,0000,0000,,ambii termeni cu un numar negativ,
Dialogue: 0,0:06:16.04,0:06:19.26,Default,,0000,0000,0000,,va trebui sa schimbati sensul inecuatiei.
Dialogue: 0,0:06:19.26,0:06:22.05,Default,,0000,0000,0000,,Cred ca sunteti gata sa incercati sa rezolvati cateva probleme.
Dialogue: 0,0:06:22.06,0:06:24.04,Default,,0000,0000,0000,,Distractie placuta .