ࡱ> VXU#` $8bjbj 4>Ahhh8<<J6$$(LLL+!+!+!5555555$7hh9j5Q+!U +!+!+!5LL 6 $ $ $+!LL5 $+!5 $ $2|6U4L , d", e" All you need to do is remember the stuff we ve already learned about inequalities: Use the same steps as with solving equations, the only difference is the inequality symbol! It just stays the same, just like the equal sign doesnt change, the inequality symbol doesnt change. UNLESS: *You multiply or divide an inequality by a negative number, * then *FLIP THE SIGN!* Assignment: pg. 191 # 1-15, pg. 197 # 1-19 Solving Inequalities Special Cases Vocabulary: Identity When solving an inequality, if you get a statement that is always true, the original inequality is an identity, and ALL REAL NUMBERS are solutions. (this means that you cancel out the variable and get an inequality that works, and infinitely many solutions [in this section, we say all real numbers instead] will be your answer) Contradiction when solving an inequality, if you get a false statement, the original inequality is a contradiction, and it has no solutions. (this means that you cancel out the variable and get an inequality that doesnt work, so no solutions will be your answer) Ok, so remember when we were solving equations and we got a problem where our variable cancelled out? Like this: x + 2 + 5x = 6x 3 + 7 2 6x + 2 = 6x + 2 combine like terms -6x -6x move the smallest variable 2 = 2 hey, they cancelled out! Now we ask, is this a true statement? If it is the answer is infinitely many solutions, if its not no solution! 2 = 2 yep, thats true! So Infinitely many solutions is my answer! With inequalities we do the same thing!     NOTES 3.4, 3.5 Page )*+-367<=>GJP_l " 6 = > F = > S ` °҇҇{҇oohFmhO>*CJaJhOhO>*CJaJhOCJaJh]fhf~5>*CJaJhf~5>*CJaJhUI"CJaJ"jhHICJUaJmHnHuhweeCJaJh CJaJhf~CJaJh<CJaJh]fh2ICJaJh]fhUI"CJaJhHICJaJ+>= >  G c q > N ` q ^gdf~ & Fgdf~gdf~8#8    G _ ` m z {     @hj诣xp诣g[PhshsCJaJhsh'>*CJaJh'>*CJaJhweeCJaJhwee5>*CJaJh]fhwee5>*CJaJ"jh'CJUaJmHnHuh'h'>*CJaJh'CJaJ"jhFmCJUaJmHnHuh2ICJaJh]fhOCJaJhFmhFm5CJaJhFmCJaJhOCJaJhf~CJaJ     4 G ` z   = Q 8gdweegd'gd2I&5QR]xyz{|}~2Twgd5|gdweegd2I$&  PRgwxy~伳ܖ܈}uc"jhs0~CJUaJmHnHuh5|CJaJh5|5>*CJaJh]fh5|5>*CJaJ"jhweeCJUaJmHnHuh]fhweeCJaJhwee5CJaJhFmhwee5CJaJhweehwee>*CJaJh7"CJaJhweeCJaJh'CJaJh ?h ?>*CJaJh ?CJaJ!LMvwEF\]?O<>@RTVf޺ޢtfh]fhf5>*CJaJ"jh{CJUaJmHnHuh{CJaJh]fh{CJaJh{5CJaJhFmh{5CJaJh]h]>*CJaJh]CJaJh'CJaJhs0~hs0~>*CJaJhweeCJaJhs0~CJaJh5|CJaJ"jh5|CJUaJmHnHu$w7EF]^r;fx>@Bgd{gd2IBDFHJLNPRVFGlmyz & Fgd g/gd g/gd >`gdfgd2Igdfgd{f0D ,6FGOklmyz{߲ߤߙ߲̑~~pep~pZpepZ~h]fh g/CJaJh g/5>*CJaJh]fh g/5>*CJaJh g/CJaJh g/hfCJaJhs0~CJaJhfhfCJaJhvVhf56CJaJhvVhf5>*CJaJhvVhf5CJaJh{CJaJhKNhfCJaJhfCJaJh]fhf5>*CJaJhf5>*CJaJ#888밨}rcarcUjh2Ih2ICJUaJh2Ih2ICJaJh2I5CJ$aJ$h1/5CJ$aJ$hf~5CJ$aJ$h2Ih2I5CJ$aJ$hMx8jhMx8Uh g/h g/CJaJh g/h g/>*CJaJh]fh g/5>*CJaJh g/5>*CJaJh]fh g/CJaJh g/CJaJh g/h g/5CJaJ!Mmg8$a$gd2I$a$gd2Igd >gd g/ & Fgd g/h^hgd g/ PAGE 4 of  NUMPAGES 4 88 8 888888888"8#8$8h g/h g/CJaJh2IhMx8hvh2Ih2ICJaJjh2Ih2ICJUaJh g/CJaJmHnHu8888 8!8"8#8$8gd >21h:p$`/ =!"#$% @@@ NormalCJ_HaJmH sH tH DAD Default Paragraph FontRiR  Table Normal4 l4a (k(No List4@4 2IHeader  !4 @4 2IFooter  !"">>=>Gcq>N`q  4G`z=QBTr5QR]xyz{|}~2Tw  7 E F ] ^ r  ; f x  ! " # $ % & ' ( ) + O    G l m y z Mmg #00000000 0 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00 0000000000000@000@000@000@000@0@0@0000P0000 0 `zQy O l y z #@0000;00:0080@00@0@0@0@000>@0@0@0@ 0@0@ 0@00w.P00000 0 @@@@@C f8$8 wB8$8#8")+0;=C!8=>@=^(  HB ) C DHB 7 C DNB 8 S DHB 9 C DD ;  "`D <  "`HB = C DB S  ?z~) ")0z`'zt70`'t8Q ! t90`'t<dnt;gnt=0`'t*-%&,-34% & #JN #3333333333#1XY]  ##Wcf4)\6}TL; > ^> `o( xx^x`hH. HLH^H`LhH. ^`hH. ^`hH. L^`LhH. ^`hH. X X ^X `hH. (#L(#^(#`LhH.z z ^z `o( xx^x`hH. HLH^H`LhH. ^`hH. ^`hH. L^`LhH. ^`hH. X X ^X `hH. (#L(#^(#`LhH.b>b^b`>o(   ^ `hH.  L ^ `LhH. xx^x`hH. HH^H`hH. L^`LhH. ^`hH. ^`hH. L^`LhH.)Wc+K(@VL;}                  (&        F        NB        i        HGLuf7"UI"nY%P&&Ko+1/ g/(@4c5Mx8QV9 ?@ F|HI2IHIdLiQVvV]weeQhFmUpPq5|u|s0~f~XX(VECmi_ vs# &}UE*O >xo $`<{'5O(1KZR[XB F KN]fs5@wL "@ @,@p@UnknownG: Times New Roman5Symbol3& : Arial"1h’F0FX1  1 !4d2QHX ?UI"2 Inequalities Humble ISD Humble ISD$      Oh+'0 $ D P \ ht|Inequalities Humble ISD Normal.dot Humble ISD15Microsoft Office Word@ K @A@?A@PF{C1՜.+,0 hp   Humble ISD    Inequalities Title !"#$%&')*+,-./0123456789:;<=>?@ABCDFGHIJKLNOPQRSTWRoot Entry FSummaryInformation(EDocumentSummaryInformation8MCompObjq  FMicrosoft Office Word Document MSWordDocWord.Document.89q