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Section%201.6 - /’ LfFe/Eiog MA 180 Precaiculus Professor...

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Unformatted text preview: /’ ' _' ' ' LfFe/Eiog MA 180 - Precaiculus Professor Terry “ '\ Section 1.6: Inequalities E] lnegualities and Interval Notation L‘ \. An inequality is a statement that two quantities are not equal. SVmbois: < H ‘5 J1“ 4“”“4‘1” >_ " Ice; fiV‘C‘UQV/Vr m“ g .. again-2.x.“ _ a u .. a m w m w waDLLcLQ +0 H Example: 7x — 1 3 6x — 1 If a true statement is obtained when a numberb is substituted for;( , thenJJ is a 30 (959‘ m of the inequality. To 60 L V6 an inequality means to find all solutions. Intervals mm Interval Notation M «m ‘ (—w—Q {if—+4.» (wt—.53... -15x§4 [—I,q’j {IE—$431» TEE—s 4““ (”NJ ‘2' 1?” -1.<_x<4 .C—Iu—I) aw“?- x>-1 (*|,oo\ é-:_‘-%‘=fiu=e_:? x34 [wi I saw - <----E'=—=‘-=>-—'? x < 4 (— 50 I am 4%» X s 4 ( we J 43 a—-£.====ff——> Open interval I ( I 3—] ' 4 Closed interval @ Half-Open intervals C 4H] W Infinite intervals (~00 I (no) MA1BO Sec1.6 SpringO4 ewt Properties of Inequalities @632; Adam gy/ 7 l g (of >/ mm— (1 Ifa<b and b<c, then a<c. (2)lfa<b, then “b - ‘5 a+c<b+canda— c<b— —c. 01+?)4 5+3 (3)Ifa<b an: c>0 then ac<bc and —<—. c c (4) lfa<b an: c<0, hen ac>bc and 3>2. C C Graph the solution set on a number line. x—8<5x+3 .534ka 5 Sunkx ’6” "-3: 0 _3 G -—u 4L: 39105 fl # «.u. < xij Dw Li (2*, «22) Li ' X >“Lfif -ci ,5 (fax) a 269 ~-- E Solving Continued Inegualities Solve the inequality, and express the solution in terms of an interval if possibie. Graph the solution set on a number line. 4x+l 3 ——Ca 4 LIX—HE: ~2< $0 Solvin Rationailn ualities Solve the inequality, and express the solution in terms of an interval if possible. Graph the solution set on a number line. Q<0=3>O IFWMfis‘ 2x+5 ”L2 “W "l 0 1' "l (a MOI/.- aoi “+5 [Jaw WMS 50 we-.." Q 3x4 5‘ :1:va (9 @¥ thS 2‘0 --OO -§—j 9X +6 < O as? I 9—) X4- Qxé-g Drug concentration To treat arrhythmia (irregular heartbeat), 3 drug is fed intravenously into the bloodstream. Suppose that the concentration c of the drug after 1‘ hours is given by c= (iii) mglL. If the minimum therapeutic level is 1. 5 mglL. determine when this level Is exceeded. Q, 3 I ‘ 5 ("g/L 3.6% > ‘3 . 53:53.53 >|,€fl+l.‘§ (W3 ' a). e Ji > l,5’ as)->u§@*b ' k_;t:>f;,3—§O t ‘ ‘2, shew—HEM (Emu } {3) Efjfg h0ww5 E Absolute Value l- a] The distance from the origin is less than 3. , (W |x|<3 is equivalent to “-3 4 X <‘ 3 ( " 3 i B) The distance form the origin is greater than 3. WWW |’x[>3 is equivalentto x‘(—5 (94/ y>3 (flag! -3) L) (BIAS) Solve the inequality, and express the solution in terms of an interval if possible. Graph the solution set on a number line. 3. Girl LL 5; 3 |x—4| s 0.03 «(a—W ~0.05 5 x~qé o 05 . 3i76x5 s03 kflel MA180 Sec1.6 Springo4 ewt Solve the inequality, and express the solution in terms of an interval if possible. Graph the solution set on a number line. I isolcflw ho . I . I 2|-11-7x|—2>10 eg—Ha—H—t—l—H—l—l—(A—r) who. \chQJwZ. (Swag Ill-m G > Lela“ "(xl m; l-ll 7N]?Co> L/ ._ —- .2: -—u- qx/L— =§\ _” “wag 1 7x7l'l fivLuanM $51- '- 4“ . 1.733 >5- “'1 7 "’1 ”'15 x £431 W X >-,. ' — -._ 'l 13? q - Trichotomy Law For any real numbers a and b exactly one of the fellowing is true: @ 0&4‘0 @ C’s-1‘0 @‘aJ'b Solvin a Quadratic lne uali Solve the inequality, and express the solutions in terms of intervals whenever possible. Graph the solution set on a number line. ' x2+4x+350 < chaDCXflQO ‘2— q‘ o 100%, a} GM 3)()£~t\10 @ch X+3z© 09 x—uzo x=~5 X=-l .€ 3% (Peek 1.1: James m f a U- .; Sign 0%: )H‘B ‘ ' 3V3“ 9Q x,” <-- r , ,fi 4' ‘ leasing Sign @ - — ‘ @ (reg—Po oars” x219 06; Li sole-mu 309‘ :[ gown 0' [say 9" MA180 Sect .6 Springo4 ewt Solve the inequalities, and express the solutions in terms of intervals whenever possible. Graph the solution set on a number line. DOW «=1; 2&5 _ L “Xx—3’20 él—l—l—«PWW? A9535 x2-9 “=32 0‘ '5 (KZ-loék 3) 30 (X43) (V‘s) 3x-t5 ACID .7“. Xi? ‘ am; \ 5“? X~a -L{(3)Lr+5_\ Q, 0 3344-2.“ apes NE? -Hx—zz=‘—o ng—tS-fi O ~uxizz Suzi-to" X2 ~7/ X4‘73 ...
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