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Let's get started. 0:00 Hello 1:20 Absolute...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/961413/f36dbc92fc2e2fa1dfc041d1b3354dff/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/HGuCSAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"17","reqid":"1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=videoid:14900067438193937081","teaser":[{"list":{"type":"unordered","items":["Bu video, Hilmi Hoca tarafından sunulan bir matematik dersidir. Öğretmen, mutlak değer konusunu detaylı bir şekilde anlatmaktadır.","Video, mutlak değer konusunun ikinci bölümünü kapsamakta olup, mutlak değer denklemleri ve eşitsizlikleri üzerine odaklanmaktadır. İçerikte mutlak değer içeren denklemlerin çözüm yöntemleri, mutlak değer eşitsizliklerinin çözüm teknikleri, mutlak değer içeren ifadelerin en büyük ve en küçük değerlerinin bulunması gibi konular ele alınmaktadır.","Videoda teorik kurallar anlatıldıktan sonra çeşitli örnek sorular çözülmekte, sayı doğrusu üzerinde mutlak değer problemlerinin çözümü gösterilmektedir. Ayrıca \"korsan metodu\" olarak adlandırılan pratik çözüm teknikleri ve günlük hayattan örneklerle konu pekiştirilmektedir. Video, TYT sınavına hazırlık amacıyla hazırlanmış olup, önceki videoda anlatılan mutlak değer özellikleri de tekrar edilmektedir."]},"endTime":2054,"title":"Mutlak Değer Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Mutlak Değer Konusunun İkinci Bölümü","list":{"type":"unordered","items":["Bu videoda mutlak değer konusunun ikinci bölümü, mutlak değerli denklemler ve eşitsizlikler ele alınacak.","Birinci bölümde mutlak değerin tanımı ve özellikleri anlatılmıştı.","Videoda pratik çözümler ve AP teknikleri uygulanacak sorular bulunmaktadır."]},"beginTime":8,"endTime":79,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=8&ask_summarization=1"},{"index":1,"title":"Mutlak Değerli Denklemler","list":{"type":"unordered","items":["Mutlak değer x, pozitif bir a sayısına eşitse, x ya a'dır ya da -a'dır.","İçerisinin pozitif mi negatif mi olduğunu bilmiyorsak, mutlak değer dışarıya çıkarken ya pozitif olarak ya da başına eksi alarak çıkar.","İki sayı arasındaki uzaklık, bu sayıların farkının mutlak değeridir."]},"beginTime":79,"endTime":138,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=79&ask_summarization=1"},{"index":2,"title":"Örnek Sorular","list":{"type":"unordered","items":["Sayı doğrusu üzerinde 2x-3 ve 11 sayıları arasındaki uzaklık 8 birim olduğunda, x'in alabileceği değerler 11 ve 3'tür.","Mutlak değer içeren denklemlerde, içerisinin pozitif mi negatif mi olduğunu bilmediğimiz için iki durum için denklem kurulur.","2019 TYT sorusunda, pozitif bir a sayısı ve sıfıra olan uzaklığı a'nın sıfıra olan uzaklığının yarısına eşit olan sayılar incelenmiştir."]},"beginTime":138,"endTime":480,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=138&ask_summarization=1"},{"index":3,"title":"Mutlak Değer Problemi Çözümü","list":{"type":"unordered","items":["İşaretlenen sayılardan birinin a sayısına uzaklığı altı birim olduğuna göre, a sayısının alabileceği değerler toplamı 16'dır.","İlk durumda x'in a'ya uzaklığı altı birim olduğunda, a sayısının değeri 12 olur.","İkinci durumda y'nin a'ya uzaklığı altı birim olduğunda, a sayısının değeri 4 olur ve toplam 16 olur."]},"beginTime":483,"endTime":612,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=483&ask_summarization=1"},{"index":4,"title":"Esprili Mutlak Değer Sorusu","list":{"type":"unordered","items":["Mutlak değer |x-5| = 2023! eşitliğinde, 2023! sayısının hesaplanamayacağı için sağ taraftaki sayı önemli değildir.","Mutlak değer |a| = a olduğunda, x = a+5 veya x = -a+5 olur ve toplamları 10'dur.","Saçma sapan sayılar (örneğin 2023! veya 2023,72) eşitliğin sağ tarafına yazıldığında, bu sayıların değeri önemli olmadığı için a şeklinde ifade edilebilir."]},"beginTime":612,"endTime":716,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=612&ask_summarization=1"},{"index":5,"title":"İç İçe Mutlak Değer Denklemi","list":{"type":"unordered","items":["İç içe mutlak değer denklemlerinde, içerisinin pozitif mi negatif mi olduğunu bilmediğimiz için dışarı çıkaramayız.","||x-2|-3| = 7 denkleminde, önce |x-2| = 7 veya |x-2| = -7 olur, bu durumda x = 9 veya x = -5 bulunur.","|x-2| = -1 denkleminde mutlak değer negatif olamayacağı için çözüm kümesi boş kümedir."]},"beginTime":716,"endTime":864,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=716&ask_summarization=1"},{"index":6,"title":"Her İki Tarafta Mutlak Değer Denklemi","list":{"type":"unordered","items":["Her iki tarafta mutlak değer olan denklemlerde, sol tarafı sabit kabul edip x'i hem y'ye hem de -y'ye eşitleriz.","|x-3| = |x+7| denkleminde, x'ler yok olduğunda geride kalan ifade yanlışsa çözüm kümesi boş kümedir.","x'ler yok olmadığında, x = 5 olarak bulunur ve çözüm kümesi {5} olur."]},"beginTime":864,"endTime":953,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=864&ask_summarization=1"},{"index":7,"title":"Mutlak Değer Eşitsizliği","list":{"type":"unordered","items":["Mutlak değerin içi dışarıya eksi olarak çıktığında, içerisi negatif veya sıfır olabilir.","|x-30| ≤ 0, |x-20| ≤ 0 denklemlerinden x ≤ 30 ve x ≥ 20 bulunur.","20'den 30'a kadar olan tam sayılar 11 tanedir."]},"beginTime":953,"endTime":1066,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=953&ask_summarization=1"},{"index":8,"title":"Mutlak Değer Eşitsizlikleri","list":{"type":"unordered","items":["Mutlak değer eşitsizliklerinde, içerisinin pozitif mi negatif mi olduğunu bilmiyorsak, klasik olarak ya aynen çıkar ya da eksi alarak çıkar diyerek soruyu çözeriz.","Pratik olarak, mutlak değer küçük olduğu zaman mutlaktan çizgilerini kaldırıp, a'nın eksilisini sol tarafa yapıştırırız.","Küçük eşittir durumunda da aynı işlemi yaparız."]},"beginTime":1069,"endTime":1114,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=1069&ask_summarization=1"},{"index":9,"title":"Mutlak Değer Eşitsizliği Örneği","list":{"type":"unordered","items":["Mutlak değer küçüktür eşitsizliğinde, mutlak değer çizgilerini kaldırıp, a'nın eksilisini sol tarafa yapıştırırız.","Çözüm kümesi iki sayı arasında çıkar ve açık aralık olarak yazılır.","Gerçek sayılardaki çözüm kümesi, aralıktaki tam sayıları içermez, sadece aralık içindeki değerleri kapsar."]},"beginTime":1114,"endTime":1167,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=1114&ask_summarization=1"},{"index":10,"title":"Sözel Mutlak Değer Sorusu","list":{"type":"unordered","items":["Sayı doğrusu üzerine bir noktaya olan uzaklık, o noktaya olan mutlak değer olarak ifade edilir.","Başlangıç noktasına uzaklık mutlak x, başka bir sayıya uzaklık ise mutlak değer x eksi o sayıdır.","Eşitsizlikte iki birimden küçük olduğu için mutlak değer çizgilerini kaldırıp, eksi ikilisini sol tarafa atarız."]},"beginTime":1167,"endTime":1227,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=1167&ask_summarization=1"},{"index":11,"title":"Hava Durumu Senaryosu","list":{"type":"unordered","items":["Bir hava durumu spikeri, pazar akşamı canlı yayında sıcaklığın beş derece olduğu kentte yarından itibaren hava ani şekilde ısınacağını açıklamıştır.","Pazartesi günü öğleden sonra kent genelinde hava sıcaklığı bir önceki güne göre altı ila on derece artmış olacak."]},"beginTime":1227,"endTime":1241,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=1227&ask_summarization=1"},{"index":12,"title":"Mutlak Değer Eşitsizlikleri","list":{"type":"unordered","items":["Hava sıcaklığı hafta boyunca 5 derece iken, önümüzdeki hafta pazartesi gününden itibaren 6 ile 10 derece artacak, bu da sıcaklığın 11 ile 15 derece arasında olacağını gösterir.","Mutlak değer eşitsizliklerinde, mutlak değerleri kaldırıp eksilisini sol tarafa yapıştırarak çözüm yapılır.","Mutlak değer büyük eşit olduğunda, içeriği pozitif veya negatif olabilir, bu durumda pozitif çıkarsa aynen çıkar, negatif çıkarsa eksi alarak çıkar."]},"beginTime":1250,"endTime":1370,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=1250&ask_summarization=1"},{"index":13,"title":"Korsan Metodu","list":{"type":"unordered","items":["Mutlak değer eşitsizliklerinde \"korsan metodu\" kullanılır: mutlak değerin çizgileri kaldırılıp eksilisi sol tarafa atılır.","Büyüktür eşitsizliğinde sonuç, küçüktür eşitsizliğindeki gibi bir şeyden küçük, bir şeyden büyük şeklinde çıkar.","Çözüm kümesi sayı doğrusunda gösterilir ve aralık şeklinde yazılır."]},"beginTime":1370,"endTime":1622,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=1370&ask_summarization=1"},{"index":14,"title":"Mutlak Değer Eşitsizliklerinde Özel Durumlar","list":{"type":"unordered","items":["Mutlak değer negatif olamaz, en küçük değeri sıfırdır ve her zaman sıfırdan büyük eşittir.","Mutlak değer büyük eşit olduğunda çözüm reel sayılar olur, ancak eşitlik yoksa içeriği sıfır yapan değer çıkarılır.","Mutlak değer küçük olduğunda çözüm boş küme olur çünkü mutlak değer negatif olamaz."]},"beginTime":1622,"endTime":1760,"href":"/video/preview/14900067438193937081?parent-reqid=1769116562641283-17630835034845725468-balancer-l7leveler-kubr-yp-klg-52-BAL&text=Tool+math+-+Topics&t=1622&ask_summarization=1"},{"index":15,"title":"Özel Soru Tipleri","list":{"type":"unordered","items":["Her iki tarafın karesini alabiliriz çünkü mutlak değerlerin sonuç itibariyle pozitif olduğunu bildiğimiz için.","Mutlak değer iki sayının arasında olduğunda, içeriği bir aynen çıkarırız ve bir de eksili çıkarırız.","Mutlak değer içeren ifadelerde, içeriğin pozitif mi negatif mi olduğunu bilmiyorsak, bir aynen çıkarırız, bir de eksili 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