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# Class Note for MATH 1300 with Professor Flagg at UH

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 12 views.

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Date Created: 02/06/15
Section 17 Notes 8 1 e gt 5mm Solving Linear Inequalities An inequality is similar to an equation except instead of an equal sign you find one of the following signs lt S gt or 2 Now gt and lt are strict inequalities and 2 and S are 39X I inequalities that include equals read these last two signs as greater than or equal to and less than or equal to respectively The solutions will be different because a linear X C X equation has one none or many solutions A linear inequality has a solution that is over I Q 39 an interval and the answers are in what is called interval notation This ensures that you have the complete answer H if X i In this section we will only be concerned with real number solutions Lager PVG L X Interval Notation Inequality Interval Notation Math 1300 H x lt A 7 00 A The rounded bracket means that A is not included x g A 7 00 A The square bracket means that A is included x gt B B 00 x23 Boo ltX lt5 34 a A lt x lt B AB A 6 A g x g B AB A Q X g5 W Intervals and the Number Line 3 a A XltH keep Wn e AgraveEV 00 H 26C A mM Wj Pr is N Inc x A W 39 gt gtlt x gtltgtB CB go 8 5500 Procedure Get X on one side by imelf or in the case of compound inequalitites get X by imelt in the middle Operations you can use to get X by itself 1 Add or subtract the SAME real number on either side all sides 2 Multiply both sides by the same POSITIVE real number 3 Divide both sides by the same POSITIVE real number Multiply or divide by aiigative number SIGN Math 1300 Section 17 Notes a Note If you multiply or divide an inequality by a negative number you have to reverse the inequality sign for the solution to be correct For examp e 7 4x gt 12 f 12 39 o 39 quot 7371quot 4 gt75 4 j x g 73 lfwe don t reverse the sign the answer will be incorrect Check the answer by testing x 1 and you get 7 471 gt 12 4 gt 12 So 1 gives the WRONG answer If we reverse the inequality we have x lt 7 3 Check this answer by testing 5 7 4 75 12 30mm x lt 3 lt gt W 20 gt12 3 q 3 So reversing the inequality gives us a TRUE statement 2gt 5 Qlt 839 IE 1 3 2132385322 W K I 4 9013 54 75 at 73 17 o 1 Q 3 4 5 Examples 1 Express the solution of 7 4x lt 8 in interval notation Egg gtlt1gt7Q 2 CO Math 1300 Section 17 Notes 2 Express the solution of 5x 7 1 g 7x 5 in interval notation 5x E 7x 5 5x fix lt O i 3 2x74 3 5 P 5 9 f0 Q S 51X 300 M Kupxin womb Goa Altgtltlt6 2ltgtltLf 45 1 4 v L Llt 4 e Qlt ltW x W MA O gt 9C Z 3 ExamEquot 3SXltO Di wlribah 5X 3X C lt 52x Likeij 9X 9 4 ax 7 QX 2gtlt Q lt Q I Ai V s X39s wosxk aidthWCr esuif7 aW 5 39Fruz j X are goldth Math1300 EVERY levSAt W umaEi Sic on17 gsLlt739W Illeka C cJ co 6 Express the solution of 7 3 g 2x 1 lt 7 in interval notation 3 2gtltl lt7 l 4 Qgtltlt 1 a I Q Z X I 2 LL 5 5 a lt gtlt 1 C 7 91 8 Express the solution of 4 7 3x g 71 8x in interval notation S7 quotTarn oe h

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