PROBLEMAS CON INECUACIONES

7/22/2019 PROBLEMAS CON INECUACIONES

1/10

^`mvnrsmhch hn Ocrtcin`c

Vrdirckcs hn Nhuocom` _upnrmdr c Hmstcòmc

Ecoultch hn mìn`mnrc, Mì. 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

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CLINJZC ] XZMI!"NXZMC XZCJC# !$:

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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

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*ZIZC"C+ M!IN!MNZMC (N 'M'XN"C' 'N"N'XZN+ M

)CZXCIN!C :63?


2/10




: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


3/10




: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


4/10




:63?


?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>


5/10




: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

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5 :

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Vcrc hcr sdluom` cplmod lc edrkulc hn7


6/10




:63?


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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 ; >


7/10




:63?


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

! " #

! " $


8/10




:63?


>7 Lc euòm` mìrnsd 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 mìrnss -r >n`tc kn`s nl ost `s hcrc lc utmlmhch -hnks hn5m`mr l smiumn`tn+

'mn`h mìrns >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


9/10




: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


10/10




:63?


Ou`tcs u`mhchns sn hnjn` vn`hnr pcrc qun lc utmlmhch snc kcydr hn $366

Z44 Lc sluom` ns

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PROBLEMAS CON INECUACIONES