Tan\u0131m say\u0131 do\u011frusu \u00fczerinde x say\u0131s\u0131n\u0131n s\u0131f\u0131ra olan uzakl\u0131\u011f\u0131na x in mutlak de\u011feri denir ve \u2502x\u2502 ile g\u00f6sterilir.<\/p>\n
x , R nin eleman\u0131d\u0131r ve \u0130SPATLAR<\/p>\n \u00d6z.1)a = 0 ise IaI = I0I = 0 Soru: I Ix-5I-2 I < 3 e\u015fitsizli\u011fini sa\u011flayan ka\u00e7 tane tamsay\u0131 vard\u0131r?\n \u00c7\u00f6z\u00fcm:I Ix-5I-2 I < 3 = -3 < Ix-5I -2 < 3\n = -1 < Ix-5I < 5\n Ix-5I >-1 e\u015fitsizli\u011fi daima do\u011frudur. Soru: I 3-3x I < 9 e\u015fitsizli\u011finin R deki \u00e7\u00f6z\u00fcm k\u00fcmesi nedir?\n\n a) 0 Soru 9: I 3x-1 I+5 = 0 denkleminin \u00e7\u00f6z\u00fcm k\u00fcmesi nedir? Ix-4I-5 =10 veya Ix-4I-5 = -10 Soru11: I Ix-1I+5 I = 8 denkleminin k\u00f6kleri toplam\u0131 ka\u00e7t\u0131r? \u00c7\u00f6z\u00fcm: I Ix-1I+5 I = 8<\/p>\n I Ix-1I+5 I = 8 veya I Ix-1I+5 = -8 Soru 12: I Ix-2I-3 I = 7 denkleminin k\u00f6kleri toplam\u0131 ka\u00e7t\u0131r? \u00c7\u00f6z\u00fcm: I Ix-2I-3 I = 7<\/p>\n Ix-2I-3 = 7 veya Ix-2I-3 = -7 Soru 13: I 7-(3-I-5I) I i\u015fleminin sonucu nedir? \u00c7\u00f6z\u00fcm: = I 7-[3-5] I Soru 14: I Ix-2I-5 I = 1 denklemini sa\u011flayan x tam say\u0131lar\u0131 nelerdir? \u00c7\u00f6z\u00fcm: I Ix-2I-5 I<\/p>\n Ix-2I-5 = 1 veya Ix-2I-5 = -1 Soru 15: Ix+2I < 4 e\u015fitsizli\u011fini sa\u011flayan ka\u00e7 tane tamsay\u0131 vard\u0131r?\n a) 13 b) 9 c) 8 d) 7 e) 6 (\u00d6SS 1999)\n \u00c7\u00f6z\u00fcm:\n Ix+2I < 4 = -4 < x + 2 <4\n = -6 < x < 2\n E\u015fitsizli\u011fi olu\u015fturan tamsay\u0131lar \u20136,-5,-4,-3,-2,-1,0,1,2 dir. ( Cevap A d\u0131r.)\n\n Soru 16: IxI < 6 oldu\u011funa g\u00f6re,x-2y+2 = 0 ko\u015fulunu sa\u011flayan ka\u00e7 tane y tamsay\u0131s\u0131 vard\u0131r?\n a) 7 b) 6 c) 5 d) 4 e) 3 (\u00d6SS 2000)\n \u00c7\u00f6z\u00fcm:\n IxI 0 dan k\u00fc\u00e7\u00fck olmayaca\u011f\u0131ndan IxI 0,1,2,3,4,5,6 olabilir.\n x-2y+2 = 0 ko\u015fulunu \u00e7ift say\u0131lar olu\u015fturur.Bunlar 0,2,4,6 d\u0131r.Bu say\u0131lar y yi tamsay\u0131 yapar. ( Cevap D dir.)\n Soru 17:\n f(x) = 12 fonksiyonunun en b\u00fcy\u00fck de\u011feri\n Ix-1I+Ix+3I\n nedir?\n a) 2 b) 3 c) 4 d) 5 e) 6\n\n \u00c7\u00f6z\u00fcm:\n x eleman\u0131d\u0131r [-3,1] i\u00e7in f(x) en b\u00fcy\u00fck olur. X = -3 ise,\n\n f(-3) = 12 = 12\/4 =3 t\u00fcr.\n I-3-1I+I-3+3I\n ( Cevap B dir.)\n\n Soru 18:\uf07cx-1\uf07c\uf0a3 6 oldu\u011funa g\u00f6re, x - 2y + 2 = O ko\u015fulunu sa\u011flayan ka\u00e7 tane y tamsay\u0131s\u0131 vard\u0131r?\n A) 7 B) 6 C) 5 D) 4 E) 3 (2000-\u00d6SS)\n \u00c7\u00d6Z\u00dcM\n x-2y + 2 = 0 => x = 2y- 2 dir. Soru 23: x < 0 < y oldu\u011funa g\u00f6re\n 3. |x-y|\n |y+|x| |\n y+ i\u015fleminin sonucu a\u015fa\u011f\u0131dakilerden hangisidir?\n A)-3x B)-3y C) 3 (x + y) D) - 3 E) 3 (1995-\u00d6SS)\n \u00c7\u00d6Z\u00dcM\n 3 |x - y| ifadesinde (x - y) < 0 oldu\u011fundan\n 3 |x - y| = - 3 (x - y) olur.\n Benzer \u015fekilde x<0 => |x| = – x olur. Tan\u0131m say\u0131 do\u011frusu \u00fczerinde x say\u0131s\u0131n\u0131n s\u0131f\u0131ra olan uzakl\u0131\u011f\u0131na x in mutlak de\u011feri denir ve \u2502x\u2502 ile g\u00f6sterilir. x , R nin eleman\u0131d\u0131r ve \u2502x\u2502 ={x, x > 0 ise {-x,x < 0 ise \u015feklinde tan\u0131mlan\u0131r. \u2502f(x)\u2502 ={f(x),f(x) > 0 ise {-f(x),f(x)< 0 ise \u00d6rnek: x =-3 i\u00e7in \u2502x-5\u2502 - \u2502x+2\u2502 ifadesinin e\u015fiti ka\u00e7t\u0131r? \u00c7\u00f6z\u00fcm: …\n<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7438,7437],"class_list":["post-3199","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-denklem","tag-mutlak-deger"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3199"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3199\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n \u2502x\u2502 ={x, x > 0 ise
\n {-x,x < 0 ise\n \u015feklinde tan\u0131mlan\u0131r.\n \u2502f(x)\u2502 ={f(x),f(x) > 0 ise
\n {-f(x),f(x)< 0 ise\n\n \u00d6rnek: x =-3 i\u00e7in \u2502x-5\u2502 - \u2502x+2\u2502 ifadesinin e\u015fiti ka\u00e7t\u0131r?\n\n \u00c7\u00f6z\u00fcm: \u2502-3-5\u2502 - \u2502-3+2 \u2502 = 8-1=7\n\n \u00d6rnek: a
\n 10)I-aI=IaI, Ia-bI=Ib-aI
\n 11)I f(x) I = a ise f(x )= a veya f(x) = -a
\n 12)I f(x) I < a ise -a< f(x) < a\n 13)I f(x) I > a ise f(x) > a U -f(x) > a<\/p>\n
\n a > 0 ise IaI = a >0
\n a < 0 ise IaI = -a >0 d\u0131r.
\n O halde IaI > 0 d\u0131r.
\n \u00d6z.2)a ve -a say\u0131lar\u0131n\u0131n 0 dan uzakl\u0131klar\u0131 e\u015fit oldu\u011fundan IaI=I-aI d\u0131r.
\n \u00d6z.6) a eleman\u0131d\u0131r R i\u00e7in -IaI \u2264 a \u2264 IaI
\n b eleman\u0131d\u0131r R i\u00e7in -IbI \u2264 b\u2264 IbI
\n +
\n -IaI-IbI\u2264a+b\u2264IaI+IbI
\n O halde Ia+bI < IaI+IbI dir.\n \u00d6z.7) a,b eleman\u0131d\u0131r R i\u00e7in Ia.bI=IaI.IbI idi.\n Ia nI=Ia.a.a...aI=IaI.IaI.IaI...IaI=IaIn dir.\n (n tane) ( n tane )\n \u00d6z.3)a say\u0131s\u0131 i\u00e7in a<0,a=0,a>0 durumlar\u0131ndan biri vard\u0131r.
\n a)a < 0 ise IaI = -a d\u0131r.\n IaI > 0 oldu\u011fundan -IaI < 0 d\u0131r.\n -IaI= a <0 < IaI ise -IaI < a < IaI d\u0131r.\n b)a=0 ise IaI = I0I = 0 ve -Ia I= 0 olaca\u011f\u0131ndan \u2013IaI < a < IaI d\u0131r.\n c)a > 0 ise IaI = a ve -IaI < 0 d\u0131r.\n -IaI\u2264 0\u2264 IaI = a ise -IaI < a < IaI d\u0131r.\n\n MUTLAK DE\u011eERL\u0130 DENKLEMLER\n Soru: I3x-7I = 5 denklemini \u00e7\u00f6z\u00fcn\u00fcz.\n \u00c7\u00f6z\u00fcm:I3x-7I = 5 ise; 3x-7 = 5 veya 3x-7 = -5 olur.\n 1- 3x-7 = 5 2- 3x-7=-5\n 3x = 12 3x = 2\n x = 4 x = 2\/3\n \u00c7={4,2\/3}\n\n Soru:Ix-7I = 7-x e\u015fitli\u011fini sa\u011flayan ka\u00e7 tane do\u011fal say\u0131 vard\u0131r?\n \u00c7\u00f6z\u00fcm: Ix-7I = 7-x ise\n x-7 < 0 ise x < 7olup x do\u011fal say\u0131lar\u0131 0,1,2,3,4,5,6,7 dir.\n O halde 8 tane do\u011fal say\u0131 vard\u0131r.\n Soru: = 2 denkleminin \u00e7\u00f6z\u00fcm k\u00fcmesi nedir ?\n\n \u00c7\u00f6z\u00fcm: = 2\n\n 5-2x\/3=2 veya 5-2x\/3= -2\n 5-2x = 6 veya 5-2x = -6\n x = -1\/2 veya x = 11\/2\n \u00c7 ={-1\/2,11\/2}\n\n\n Soru:I 4+I2x-3I I = 5 denklemini sa\u011flayan x reel say\u0131lar\u0131n\u0131n toplam\u0131 nedir?\n \u00c7\u00f6z\u00fcm: I 4+I2x-3I I = 5\n\n 4+I2x-3I = 5 veya 4+I2x-3I = -5\n I2x-3I = 1 veya I2x-3I = -9\n\n 2x-3 = 1 veya 2x-3 = -1 \u00c7\u00f6z\u00fcm\n\n x = 2 x = 1\n\n O halde x+x = 2+1 = 3 olur.\n Uyar\u0131:Hi\u00e7bir reel say\u0131n\u0131n mutlak de\u011feri negatif olamayaca\u011f\u0131ndan, denklemin \u00e7\u00f6z\u00fcm k\u00fcmesi bo\u015f k\u00fcme () olur.\n\n MUTLAK DE\u011eERL\u0130 E\u015e\u0130TS\u0130ZL\u0130KLER\n\n\n Soru: Ix-7I < 3 e\u015fitsizli\u011finin \u00e7\u00f6z\u00fcm k\u00fcmesini bulunuz.\n\n \u00c7\u00f6z\u00fcm: Ix-7I < 3 = -3 < x-7 < 3 = -3+7 < x < 3+7\n =4
\n \u00c7\u00f6z\u00fcm:I 3x+2I+9 > 2 = I 3x+2I > -7
\n ***Bu e\u015fitsizlik x in her de\u011feri i\u00e7in sa\u011flan\u0131r.Bu nedenle; \u00c7\u00f6z\u00fcm k\u00fcmesi R dir.<\/p>\n
\n Ix-5I < 5 = -5 < x-5 < 5\n = 0 < x < 10\n Bu aradaki tamsay\u0131lar 1,2,3,4,5,6,7,8,9 olup 9 tamsay\u0131 vard\u0131r.\n\n Soru: I 2x-7 I < 2 e\u015fitsizli\u011fini sa\u011flayan ka\u00e7 tane tamsay\u0131 vard\u0131r?\n\n \u00c7\u00f6z\u00fcm:I 2x-7 I < 2 = -2 < 2x-7 < 2\n = -2+7 < 2x < 2+7\n = 5 < 2x < 9\n = 5\/2 < x < 9\/2\n Bu durumda \u00e7\u00f6z\u00fcm k\u00fcmesi {3,4} olur.\n\n Soru: I 3x+1 I > -8 denkleminin \u00e7\u00f6z\u00fcm k\u00fcmesini bulunuz.
\n \u00c7\u00f6z\u00fcm: x eleman\u0131d\u0131r R i\u00e7in I 3x+1 I > 0 oldu\u011fundan
\n I 3x+1 I > -8 e\u015fitsizli\u011fi daima do\u011frudur. Buna g\u00f6re denklemin \u00e7\u00f6z\u00fcm k\u00fcmesi Reel say\u0131lar k\u00fcmesidir.<\/p>\n
\n x = 4 veya x = -2 dir.
\n Soru 6: a
\n \uf07cx\uf07c = 8 veya \uf07cx\uf07c = 2
\n x = 8 veya x =- 8 veya
\n x = 2 veya x =- 2 dir.
\n \u00c7.K. = {-8, -2, 2, 8} dir.
\n Soru 8: ||x-l| + 4| = 6=>\uf07cx-1\uf07c + 4 = 6 veya
\n \uf07cx-1\uf07c + 4 = -6 lx-1l = 2 veya lx-1l = -10 olur.
\n \uf07cx-1\uf07c = – 10 olamayaca\u011f\u0131ndan k\u00f6k yoktur.
\n \uf07cx-1\uf07c = 2 ise x – 1 = 2 veya x – 1 = -2 x = 3 veya x = -1 dir.
\n \u00c7.K = {-1,3}<\/p>\n
\n \u00c7\u00f6z\u00fcm: I 3x-1 I+5 = 0 ise I 3x-1 I = -5 olur.
\n *** a eleman\u0131d\u0131r R i\u00e7in IaI > 0 d\u0131r.
\n Bu nedenle sorunun \u00e7\u00f6z\u00fcm k\u00fcmesi O dir.
\n Soru 10: I Ix-4I -5 I = 10 denklemini sa\u011flayan x de\u011ferlerini bulunuz.
\n \u00c7\u00f6z\u00fcm: I Ix-4I \u20135 I = 10<\/p>\n
\n Ix-4I = 5 veya Ix-4I = -5
\n \u00c7 = {O}
\n x-4 = 15 veya x-4 = -15 x = 19 veya x = -14<\/p>\n
\n a) -2 b) 0 c) 2 d) 4 e)14<\/p>\n
\n Ix-1I = 3 veya Ix-1I = -13
\n \u00c7 = {O}
\n x-1 = 3 veya x-1 = -3
\n x = 4 veya x = -2
\n x+x = 4+(-2) = 2 ( Cevap C dir.)<\/p>\n
\n a) 2 b) 4 c) 8 d) 10 e) 12<\/p>\n
\n Ix-2I = 10 veya Ix-2I = -4
\n \u00c7 = {O}
\n x-2 = 10 veya x-2 = -10
\n x = 12 veya x = -8
\n x+x = 12-(-8) = 4 ( Cevap B dir.)<\/p>\n
\n A) 4 B) 5 C) 6 D) 7 E) 9<\/p>\n
\n I 7-(3-I-5I) I = I 7-[3- -(-5)] I<\/p>\n
\n = I 7-(-2) I
\n = I 7+2 I
\n = I 9 I = 9<\/p>\n
\n a) 3,6,-3,-6 b) 4,8,-3,-8 c) 7,9,5 d) 8,-4,6,-2 e) 2,-2<\/p>\n
\n Ix-2I = 6 veya Ix-2I = 4
\n x-2 = 6 veya x-2 = -6 x-2 = 4 veya x-2 = -4
\n x = 8 x = -4 x = 6 x = -2<\/p>\n
\n \uf0bdx\uf0bd < 6 => \uf0bd2y – 2\uf0bd 6 => -6 \uf0a3 2y – 2 < 6 d\u0131r.\n Buradan, -4 < 2y < 8 => -2 < y < 4 bulunur.\n Bu ko\u015fulu sa\u011flayan y tamsay\u0131lar\u0131 -2, -1, 0, 1, 2, 3, 4 olup 7 tanedir.\n Cevap: A'd\u0131r.\n\n Soru 19:\uf0bdx+2\uf0bd\uf0a34 e\u015fitsizli\u011fini sa\u011flayan ka\u00e7 tane tamsay\u0131 vard\u0131r?\n A) 13 B) 9 C) 8 D) 7 E) 6 (1999-\u00d6SS)\n\n \u00c7\u00d6Z\u00dcM\n \uf0bdx+2\uf0bd\uf0a34 ise < 4 ise -4 < x + 2 < 4\n -4-2
\n 0 < x < 4 i\u00e7in, -x + 4 + x = 8 olur.\n 4 = 8 oldu\u011fundan bu aral\u0131kta sa\u011flayan x de\u011feri yoktur. x > 4 i\u00e7in, x – 4 + x = 8 olur.
\n 2x = 12 => x = 6 d\u0131r.
\n x de\u011ferleri toplam\u0131 -2 + 6 = 4 olur.
\n Cevap: B’dir.<\/p>\n
\n | y + |x| | = |y-x| = y-x
\n +
\n 3(x-y) = -3(x-y) =3
\n y-x -(x-y)
\n Cevap: E’dir<\/p>\n","protected":false},"excerpt":{"rendered":"