PROBLEMAS CON INECUACIONES
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Transcript of PROBLEMAS CON INECUACIONES
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c 3
VZDIZCKC HN M@IN@MNZMC HN _M_XNKC_ KDHCLMHCH C HM_XC@OMC
IZ^VD M3- KCC@C
XNKC7
CLINJZC ] XZMI!"NXZMC XZCJC# !$:
N_X^HMC@XN7
KCZOD_ C^ZNLMD KCZX@NW VZXNLD 83>3?:6683
HNMKNZ KN@HDWC ]C@NW 83>3?:66?=KCZMD HCUMLC HCUMLC 83>3?:6638
KCZMC COD_XC _CLC_ 83>3?:66?>@CHMC G^LMD KNHZC@D 83>3?:6658
CLNRM_ VNHZDWC 83>3?:6665
X^XDZ7
CZKC@HD JCXM_XC
%!M&NZ'M(C( (N )CZXCIN!C
EC)%LXC( (N N(%)C)M! CJMNZXC ] C (M'XC!)MC
*ZIZC"C+ M!IN!MNZMC (N 'M'XN"C' 'N"N'XZN+ M
)CZXCIN!C :63?
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c :
XZCJCGD @
J#NXM&+ C-lmocr lc tnrc somclm/chc n` lcs tutrcs n` lc rnsluom` hn -rlnkcs
37 ^`c eurid`ntc pnsc 29> ai. Lc hmenrn`omc n`trn nl pnsd hn lc eurid`ntc vcoc y nl pnsd hnlc ocric qun llnvn `d hnjn snr m`enrmdr qun 83> ai. _m bcy qun ocricr ouctrd ocgd`ns miuclns,ou`td punhn pnscr, odkd kxmkd, ochc u`d hn nllds pcrc pdhnr llnvcrlds n` nsceurid`ntc4
Eurid`ntc pnsc ; 29> ai.
R; ocric
29> x 83> aiOcric ; 8 y (ouctrd ocgd`ns od` pnsds miuclns scjmn`hd qun y ns nl pnsd)
R; 8y
29> -8 y 83>8 83>29>
8 856
8568 33>
Ou`td punhn pnscr, odkd kxmkd, ochc u`d hn nllds pcrc pdhnr llnvcrlds n` nsceurid`ntc4 Z\\ su pnsd hnjn snr hn 33> ai
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c ?
:7 ^`c ejrmoc pcic c sus vmcgc`tns $36 pdr crtould vn`hmhd ks u`c oc`tmhch emgc hn$>66.Dtrc ejrmoc hn lc odkpntn`omc pcic $3> pdr crtould y $?66 emgcs. Ou`tds crtouldshnjn vn`hnr nl vmcgc`tn hn lc odkpntn`omc pcrc ic`cr ks hm`nrd qun nl prmknrd4.
Ecjrmoc 37 36x +>66
Ecjrmoc :7 3>x +?66
_mn`hd x ; crtoulds.
Vdhnkds cemrkcs qunVcrc qun nl vmcgc`tn : hn lc ecjrmoc : ic`n ks qun lc ecjrmoc 3 sn nstcjlnon lc smiumn`tnm`noucom`.
36x +>66 x + ?6636x -3>x
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c 8
?7 C`c y Jnctrmz prnpcrc` pcstnlns. _m nl trmpln hn ld qun prnpcrc C`c ks ld hn Jnctrmz nskcydr qun >3 y, sm chnks nl hdjln hn C`c kn`ds ld hn Jnctrmz ns :8, Oul ns lc oc`tmhchk`mkc hn pcstnlns qun punhn` bconr gu`tcs4
C`c y Jnctrmz prnpcrc` pcstnlns.
Hmickds qun pcstnlns hn c`c ;x
Hmickds qun pcstnlns hn Jnctrmz ;y
(3) ?x + y 0>3(:) :x y ; :8
_cjmn`hd ld c`tnrmdr hnspngckds noucom` hds7
:x y ; :8 tn`nkds hnspngc`hd n` y :x -:8 ; y
Znkplczc`hd 3> ; x n` noucom` (: )tn`nkds.
:x y ; :8
: (3>)- y ; :8
?6 y ; :8
?6 :8 ; y
5 ; y
_ustmtuyn`hd n` noucom` (3) tn`nkds7
?x + y 0>3?x + (:x-:8)>3
>x -:8 >3
>x > 3 : 8
>x 9>
x 3>
Xn`nkds.
Sun lc oc`tmhch k`mkc hn Jnctrmz sd` 5pcstnlns.
lc oc`tmhch k`mkc hn C`c ns 3>
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c >
Oul ns lc oc`tmhch k`mkc hn pcstnlns qun punhn` bconr gu`tcs4
Z \\ 3> pcrc C`c y 5 pcrc Jnctrmz. N` tdtcl punhn` bconr 3> +5 ; :3 pcstnlns odkd k`mkd
87 Nl odstd hn prdhuoom` hn x u`mhchns hn u` prdhuotd nst hchd pdr lc nxprnsm`:
5O x x; + , lc utmlmhch pdr od`onptd hn vn`tcs nst hchc pdr ::^ x x; + . Ou`tcsu`mhchns sn hnjn` vn`hnr pcrc djtn`nr utmlmhch
_cjmn`hd qun
Nl odstd ns7
:5O x x; +
y lc utmlmhch ns7
::^ x x; +
Vdhnkds hnomr qun pcrc djtn`nr utmlmhch nl odstdhnjn snr kn`dr qun lc utmlmhch.
N`td`ons tn`nkds7
5 :
5 :
: 5
>
6 >
Vcrc hcr sdluom` cplmod lc edrkulc hn7
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c 5
;
8:
_mn`hd C ; 3
J ; ->
O ; 6
; (>) (>)
8 ( 6 3 ):(3) ; (+>) : > 6:
; (+>) :>:
; (+>)>:
3 ; (+>) + >: ; >
; (+>) >: ; 6
N`td`ons pdhnkds hnomr qun 7
6 < > + ; (x ->) (x+6)6 )6 ) ; 6 x ; >
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c 9
x+6 ; 6 x ;6
_DL^OMD@7
(-!6 " (>,)
Ou`tcs u`mhchns sn hnjn` vn`hnr pcrc djtn`nr utmlmhch4
_dlckn`tn tdkc`hd u`mhchns pdsmtmvcs pdhnkds cemrkcr ld smiumn`tn, sn hnjn` vn`hnr ks hnom`od u`mhchns pcrc djtn`nr utmlmhch.
> x
6
! " #
! " $
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c 2
>7 Lc eu`om` m`irnsd pdr vn`tc hn u` prdhuotd nst hchd pdr lc nxprnsm` 86 #$ . Nlodstd hn prdhuoom` hn u`c u`mhch ns hn $:2. Ou`tcs u mhchns sn hnjn` vn`hnr pcrcqun lc utmlmhch snc kcydr hn $366
'm scnks 8un ls m`irnss -r >n`tc kn`s nl ost `s hcrc lc utmlmhch -hnks hn5m`mr l smiumn`tn+
'mn`h m`irns >n`tc 9 86 #$ ] osts hn -rhuoom` 9 :2=
*hnks hn5m`mr ls smiumn`tn 9 %86 :> & :2 0366
'86:
> :2366 06
'3: :> 366 06
'56 : >66 06(ns-n7c`h cl tr lch hn lc miuclhch.
': 56 +>66
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c =
'mn`h 9 16
'mn`h o 9 66
;56 56 83>66
:3
;56 )566:666
:
; 56 3566:
;56 3566
:
;5686
:
3 ;56 86
:; >6
: ;56 86
:; 36
'mn`h nst -hnks hnomr 8un
*: 56 + >66 6 9
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7/22/2019 PROBLEMAS CON INECUACIONES
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^`mvnrsmhch hn Ocrtcin`c
Vrdirckcs hn Nhuocom` _upnrmdr c Hmstc`omc
Ecoultch hn m`in`mnrc, M`i. hn smstnkcs
:63?
Clnhrdzc vmnr`ns, 63 hn `dvmnkjrn hn :63? Vim`c 36
Ou`tcs u`mhchns sn hnjn` vn`hnr pcrc qun lc utmlmhch snc kcydr hn $366
Z44 Lc sluom` ns