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Ödüllü sorunun cevabını bir sonraki videoda...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3354973/5c4f0c76167fedb5f51315b8ac7ed835/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/ri82AwAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"2","reqid":"1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=videoid:10040148827624614589","teaser":[{"list":{"type":"unordered","items":["Kampüs kanalından bir matematik öğretmeninin mutlak değer eşitsizlikleri konusunu anlattığı eğitim videosu.","Video, mutlak değer eşitsizliklerinin çözüm kurallarını teorik olarak açıklayarak başlıyor ve ardından çeşitli örneklerle pekiştiriyor. Öğretmen, mutlak değerli ifadelerin bir sayıdan küçük veya büyük olması durumlarını, birden fazla mutlak değerli ifadenin bulunduğu eşitsizlikleri ve ikinci dereceden eşitsizlikleri çözüm yöntemlerini adım adım anlatıyor.","Videoda ayrıca çözüm aralıklarının sayı doğrusu üzerinde gösterilmesi, işaret tablosu yöntemi, mutlak değerden kurtulma yöntemleri ve çözüm kümesinin farklı gösterimlerle (yuvarlak parantez, köşeli parantez) açıklanması gibi konular ele alınıyor. Video, ödüllü sorularla interaktif bir şekilde ilerleyerek öğrencilere konuyu pekiştirmeleri için fırsatlar sunuyor."]},"endTime":2062,"title":"Mutlak Değer Eşitsizlikleri Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Mutlak Değer Eşitsizliklerinin Çözüm Kuralları","list":{"type":"unordered","items":["Mutlak değer eşitsizliklerinin çözüm kuralları anlatılacaktır.","Bir mutlak değerli ifade bir pozitif gerçek sayıdan küçükse, mutlak değerin içerisindeki ifade sayının eksi ve artılısı aralığına sıkıştırılır.","Eşitsizlikte eşitlik işareti varsa, açılımında da eşitlik olacaktır."]},"beginTime":8,"endTime":66,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=8&ask_summarization=1"},{"index":1,"title":"Negatif Sayılar İçin Mutlak Değer Eşitsizlikleri","list":{"type":"unordered","items":["Eğer a negatif bir sayı olursa, mutlak değer eşitsizliğinin çözüm aralığı boş küme olacaktır.","Mutlak değerli bir ifadenin sonucu daima pozitif olduğundan, negatif bir sayıdan küçük olamaz."]},"beginTime":66,"endTime":94,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=66&ask_summarization=1"},{"index":2,"title":"Alıştırmalar","list":{"type":"unordered","items":["İlk alıştırmada |2x-5|\u003c7 eşitsizliğini sağlayan x tam sayı değerleri 6 tane bulunmuştur.","İkinci alıştırmada |384|\u003c-2 eşitsizliğinin çözüm kümesi boş küme olarak belirlenmiştir.","Üçüncü alıştırmada |2a-1|\u003c11 ve 3b=4 koşullarına göre b'nin alabileceği tam sayı değerlerinin toplamı 3 olarak hesaplanmıştır."]},"beginTime":94,"endTime":316,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=94&ask_summarization=1"},{"index":3,"title":"Mutlak Değer Eşitsizlikleri","list":{"type":"unordered","items":["Mutlak değer içeren eşitsizliklerde, aynı mutlak değerlerin toplamının bulunduğu durumlarda, mutlak değerlerin aynı olduğunu göstermek yeterlidir.","Mutlak değer içeren eşitsizliklerde, mutlak değer içindeki ifadenin belirli aralıklarda sıkıştırılması gerekir.","Mutlak değer içeren eşitsizliklerin çözümünde, mutlak değer içindeki ifadenin belirli aralıklarda sıkıştırılması ve eşitsizliğin her iki tarafına aynı sayı eklenmesi veya çıkarılması gerekir."]},"beginTime":322,"endTime":487,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=322&ask_summarization=1"},{"index":4,"title":"Mutlak Değer Eşitsizliklerinde Değer Aralığı","list":{"type":"unordered","items":["Mutlak değer içeren eşitsizliklerde, x'in değer aralığı bulunurken, mutlak değer içindeki ifadenin belirli aralıklarda sıkıştırılması gerekir.","Mutlak değer içeren eşitsizliklerde, x'in değer aralığı bulunurken, mutlak değer içindeki ifadenin belirli aralıklarda sıkıştırılması ve eşitsizliğin her iki tarafına aynı sayı eklenmesi veya çıkarılması gerekir.","Mutlak değer içeren eşitsizliklerde, x'in değer aralığı bulunurken, mutlak değer içindeki ifadenin belirli aralıklarda sıkıştırılması ve eşitsizliğin her iki tarafına aynı sayı eklenmesi veya çıkarılması gerekir."]},"beginTime":487,"endTime":601,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=487&ask_summarization=1"},{"index":5,"title":"Mutlak Değerin Pozitif Sayıdan Büyük Olması","list":{"type":"unordered","items":["Mutlak değer içindeki ifadenin pozitif bir sayıdan büyük olması durumunda, iki durum değerlendirilir: mutlak değer içindeki ifade pozitif sayıdan büyük olabilir veya negatif sayıdan küçük olabilir.","Mutlak değer içindeki ifadenin pozitif bir sayıdan büyük olması durumunda, çözüm aralığı tüm gerçel sayılar olabilir.","Mutlak değer içindeki ifadenin pozitif bir sayıdan büyük olması durumunda, çözüm aralığı tüm gerçel sayılar olabilir."]},"beginTime":601,"endTime":717,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=601&ask_summarization=1"},{"index":6,"title":"Mutlak Değer Eşitsizliklerinin Sayı Doğrusunda Gösterimi","list":{"type":"unordered","items":["Mutlak değer içeren eşitsizliklerin çözüm aralığı bulunurken, mutlak değer içindeki ifadenin belirli aralıklarda sıkıştırılması gerekir.","Mutlak değer içeren eşitsizliklerin çözüm aralığı bulunurken, mutlak değer içindeki ifadenin belirli aralıklarda sıkıştırılması ve eşitsizliğin her iki tarafına aynı sayı eklenmesi veya çıkarılması gerekir.","Mutlak değer içeren eşitsizliklerin çözüm aralığı bulunurken, mutlak değer içindeki ifadenin belirli aralıklarda sıkıştırılması ve eşitsizliğin her iki tarafına aynı sayı eklenmesi veya çıkarılması gerekir."]},"beginTime":717,"endTime":821,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=717&ask_summarization=1"},{"index":7,"title":"Eşitsizliklerde Çözüm Aralığı","list":{"type":"unordered","items":["Eşitsizliklerde çözüm aralığında dahil olacak değerler parantez içinde gösterilir, dahil olmayan değerler ise parantez dışında gösterilir.","Reel sayılardan dışarıya atılan bölgede sınır değerleri çıkartılmaz."]},"beginTime":824,"endTime":873,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=824&ask_summarization=1"},{"index":8,"title":"Eşitsizliklerde Kurnazlık","list":{"type":"unordered","items":["Eşitsizliği sağlamayan x tam sayı değerlerinin toplamını bulmak için, büyük eşitsizliği sağlayanları bulmak yerine, küçük eşitsizliği sağlamayanları bulmak daha kolaydır.","Büyüktürün tersi küçük eşittir, küçük eşittirin tersi büyüktür şeklinde ifade edilir."]},"beginTime":873,"endTime":925,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=873&ask_summarization=1"},{"index":9,"title":"Mutlak Değerli Eşitsizlikler","list":{"type":"unordered","items":["Mutlak değerli bir ifadenin mutlak değerli bir ifadeden küçük olduğu durumda, her iki tarafın karesini alarak mutlak değerlerden kurtulup normal bir eşitsizlik çözümüne geçilir.","İki tarafta birden pozitif sayı varsa, eşitsizliklere dokunmadan mutlak değerli ifadeyi dışarı çıkartıp, bir artı bir eksiği dışarı çıkartarak iki aralıkta çözüm yapılır."]},"beginTime":925,"endTime":1103,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=925&ask_summarization=1"},{"index":10,"title":"Eşitsizliklerde Çözüm Örnekleri","list":{"type":"unordered","items":["Eşitsizliklerde çözüm yaparken, eşitsizliklere dokunmadan mutlak değerli ifadeyi dışarı çıkartıp, bir artı bir eksiği dışarı çıkartarak iki aralıkta çözüm yapılır.","İki tarafta birden mutlak değerli ifade varsa, her iki tarafın karesini alarak mutlak değerlerden kurtulup normal bir eşitsizlik çözümüne geçilir."]},"beginTime":1103,"endTime":1380,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=1103&ask_summarization=1"},{"index":11,"title":"Mutlak Değer Eşitsizliği Çözümü","list":{"type":"unordered","items":["Bir sayı doğrusunda x sayısının -4 noktasına uzaklığı, 2 noktasına uzaklığının iki katından daha küçük olduğuna göre x'in değer aralığı bulunması isteniyor.","x sayısının -4 noktasına uzaklığı |x+4| olarak ifade edilir çünkü a'nın b noktasına uzaklığı |a-b| formülüyle hesaplanır.","Eşitsizlik |x+4| \u003c 2|x-2| şeklinde yazılır ve her iki tarafın karesi alınarak mutlak değerlerden kurtulunur."]},"beginTime":1382,"endTime":1466,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=1382&ask_summarization=1"},{"index":12,"title":"İkinci Dereceden Eşitsizliğin Çözümü","list":{"type":"unordered","items":["Eşitsizliğin her iki tarafının karesi alınarak x²+8x+16 \u003c 4x²-24x+16 eşitsizliği elde edilir.","Eşitsizlik düzenlenerek 3x²-24x > 0 şeklinde ikinci dereceden bir eşitsizliğe dönüşür.","İşaret tablosu oluşturulduğunda, ifadenin sıfırdan büyük olduğu bölgeler (-∞,0) ∪ (8,∞) olarak bulunur."]},"beginTime":1466,"endTime":1566,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=1466&ask_summarization=1"},{"index":13,"title":"Çözüm Kümesinin Gösterimi","list":{"type":"unordered","items":["Çözüm kümesi reel sayılar fark (0,8) şeklinde köşeli parantezlerle gösterilebilir.","Köşeli parantezler, eşitsizliği sağlayan değerlerin aralığında ve 8'in dahil olmadığını gösterir.","Çözüm kümesi ayrıca (0,8) şeklinde de gösterilebilir."]},"beginTime":1566,"endTime":1624,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=1566&ask_summarization=1"},{"index":14,"title":"Mutlak Değerden Kurtulma Yöntemi","list":{"type":"unordered","items":["Mutlak değer içeren bir soruda, mutlak değerden kurtulmak için farklı bir yöntem kullanılır.","Mutlak değer içeren ifadenin içi sıfırdan büyük, sıfırdan küçük veya sıfıra eşit olabilir.","İki x eksi beş ifadesinin sıfırdan büyük olduğu durumda x'in 5/2'den büyük olduğu, sıfırdan küçük eşit olduğu durumda ise 5/2'den küçük eşit olduğu bulunur."]},"beginTime":1627,"endTime":1734,"href":"/video/preview/10040148827624614589?parent-reqid=1769636662050385-7601823325493294982-balancer-l7leveler-kubr-yp-vla-25-BAL&text=daXoder+M%40x&t=1627&ask_summarization=1"},{"index":15,"title":"Çözüm Kümesinin Belirlenmesi","list":{"type":"unordered","items":["Sayı doğrusu üzerinde x'in 5/2'den büyük olduğu durumda çözüm kümesi 5/2'den 9'a kadar olan aralıktır.","x'in 5/2'den küçük eşit olduğu durumda çözüm kümesi 5/2'den 1/3'e kadar olan aralıktır.","İki çözüm kümesi birleştirildiğinde, eşitsizliğin çözüm kümesi 1/3 ile 9 aralığında bulunan 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