34:@0.058599:0.966558:0.074760:0.966558:0.074760:0.950778:0.058599:0.950778:0.000000:0.000000
Ecuaciones e inecuaciones de primer :@0.404235:0.120539:0.859213:0.120539:0.859213:0.075879:0.404235:0.075879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
grado con valor absoluto:@0.404235:0.158258:0.711658:0.158258:0.711658:0.113598:0.404235:0.113598:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.8. Aplicar las propiedades de orden de los números reales para resolver ecuaciones e inecuaciones de primer grado con una incógnita y con valor absoluto.:@0.143847:0.955611:0.836169:0.955611:0.836169:0.945569:0.143847:0.945569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.404236:0.182194:0.484320:0.182194:0.484320:0.165248:0.404236:0.165248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sea :@0.484322:0.181731:0.519481:0.181731:0.519481:0.165233:0.484322:0.165233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.519481:0.181847:0.532601:0.181847:0.532601:0.165378:0.519481:0.165378:0.000000:0.000000
:@0.532601:0.181514:0.548649:0.181514:0.548649:0.166867:0.532601:0.166867:0.000000
   . El valor absoluto de   se designa con | | y se :@0.548649:0.181731:0.895918:0.181731:0.895918:0.165233:0.548649:0.165233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.552791:0.180762:0.566700:0.180762:0.566700:0.167315:0.552791:0.167315:0.000000
a:@0.721550:0.181847:0.730528:0.181847:0.730528:0.165378:0.721550:0.165378:0.000000
a:@0.847119:0.181847:0.856097:0.181847:0.856097:0.165378:0.847119:0.165378:0.000000
define como::@0.404236:0.199082:0.497613:0.199082:0.497613:0.182584:0.404236:0.182584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| | = :@0.579415:0.222520:0.617503:0.222520:0.617503:0.206022:0.579415:0.206022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.584424:0.222635:0.593402:0.222635:0.593402:0.206167:0.584424:0.206167:0.000000
a,   a :@0.624265:0.216866:0.667245:0.216866:0.667245:0.200397:0.624265:0.200397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si ≥ 0,:@0.639927:0.216751:0.693446:0.216751:0.693446:0.200253:0.639927:0.200253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–a,  a :@0.624265:0.234217:0.677283:0.234217:0.677283:0.217748:0.624265:0.217748:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si  < 0.:@0.649965:0.234101:0.703483:0.234101:0.703483:0.217604:0.649965:0.217604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.404236:0.265147:0.534891:0.265147:0.534891:0.248360:0.404236:0.248360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  :@0.404236:0.289467:0.424677:0.289467:0.424677:0.272752:0.404236:0.272752:0.000000:0.000000:0.000000:0.000000
Si   = 3 > 0; entonces |3| = 3.:@0.427971:0.289250:0.632684:0.289250:0.632684:0.272752:0.427971:0.272752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.443923:0.289365:0.452900:0.289365:0.452900:0.272897:0.443923:0.272897:0.000000
2.  :@0.404236:0.313946:0.424677:0.313946:0.424677:0.297231:0.404236:0.297231:0.000000:0.000000:0.000000:0.000000
Si   = –3 < 0; entonces |–3| = –(–3) = 3.:@0.427971:0.313729:0.714176:0.313729:0.714176:0.297231:0.427971:0.297231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.443923:0.313844:0.452900:0.313844:0.452900:0.297376:0.443923:0.297376:0.000000
3. :@0.404236:0.350585:0.420592:0.350585:0.420592:0.333870:0.404236:0.333870:0.000000:0.000000:0.000000
Si   = :@0.427971:0.350368:0.471992:0.350368:0.471992:0.333870:0.427971:0.333870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.443923:0.350483:0.452900:0.350483:0.452900:0.334015:0.443923:0.334015:0.000000
–3:@0.476503:0.344076:0.495498:0.344076:0.495498:0.327578:0.476503:0.327578:0.000000:0.000000
2:@0.481762:0.360415:0.490258:0.360415:0.490258:0.343917:0.481762:0.343917:0.000000
 <0, entonces :@0.500006:0.350351:0.599201:0.350351:0.599201:0.333854:0.500006:0.333854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–3:@0.603993:0.343116:0.622989:0.343116:0.622989:0.326618:0.603993:0.326618:0.000000:0.000000
2:@0.609253:0.359454:0.617749:0.359454:0.617749:0.342957:0.609253:0.342957:0.000000
 = – :@0.627351:0.350363:0.661085:0.350363:0.661085:0.333865:0.627351:0.333865:0.000000:0.000000:0.000000:0.000000:0.000000
–3:@0.666976:0.342819:0.686164:0.342819:0.686164:0.326321:0.666976:0.326321:0.000000:0.000000
2:@0.672331:0.359157:0.680827:0.359157:0.680827:0.342660:0.672331:0.342660:0.000000
 =   :@0.692059:0.350352:0.729532:0.350351:0.729532:0.333854:0.692059:0.333854:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.714023:0.344076:0.722519:0.344076:0.722519:0.327578:0.714023:0.327578:0.000000
2:@0.714023:0.360415:0.722519:0.360415:0.722519:0.343917:0.714023:0.343917:0.000000
4.  :@0.404238:0.382175:0.424678:0.382175:0.424678:0.365461:0.404238:0.365461:0.000000:0.000000:0.000000:0.000000
Si   = 0; entonces |0| = 0.:@0.427973:0.381959:0.605097:0.381959:0.605097:0.365461:0.427973:0.365461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.443924:0.382074:0.452902:0.382074:0.452902:0.365606:0.443924:0.365606:0.000000
Propiedades del valor absoluto:@0.404236:0.421676:0.651596:0.421676:0.651596:0.403993:0.404236:0.403993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema. :@0.404236:0.438846:0.479735:0.438846:0.479735:0.421901:0.404236:0.421901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.479735:0.438384:0.517533:0.438384:0.517533:0.421886:0.479735:0.421886:0.000000:0.000000:0.000000:0.000000:0.000000
a, b :@0.517533:0.438499:0.546604:0.438499:0.546604:0.422031:0.517533:0.422031:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.546604:0.438167:0.562652:0.438167:0.562652:0.423520:0.546604:0.423520:0.000000
  . Se verifican las siguientes propiedades::@0.562652:0.438384:0.859335:0.438384:0.859335:0.421886:0.562652:0.421886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.566794:0.437415:0.580704:0.437415:0.580704:0.423968:0.566794:0.423968:0.000000
i) :@0.404236:0.463499:0.418859:0.463499:0.418859:0.446784:0.404236:0.446784:0.000000:0.000000:0.000000
| | ≥ 0.:@0.427971:0.463282:0.477309:0.463282:0.477309:0.446784:0.427971:0.446784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.432980:0.463398:0.441958:0.463398:0.441958:0.446929:0.432980:0.446929:0.000000
ii) :@0.404236:0.487978:0.423116:0.487978:0.423116:0.471263:0.404236:0.471263:0.000000:0.000000:0.000000:0.000000
| | = 0     = 0.:@0.427971:0.487761:0.539889:0.487757:0.539889:0.471259:0.427971:0.471263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.432980:0.487877:0.441958:0.487877:0.441958:0.471408:0.432980:0.471408:0.000000
a:@0.500568:0.487872:0.509546:0.487872:0.509546:0.471404:0.500568:0.471404:0.000000
iii) :@0.404242:0.512453:0.427380:0.512453:0.427380:0.495738:0.404242:0.495738:0.000000:0.000000:0.000000:0.000000:0.000000
| | = | | | |.:@0.427977:0.512236:0.520392:0.512236:0.520392:0.495738:0.427977:0.495738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ab:@0.432986:0.512351:0.451114:0.512351:0.451114:0.495883:0.432986:0.495883:0.000000:0.000000
a b:@0.480224:0.512351:0.512628:0.512351:0.512628:0.495883:0.480224:0.495883:0.000000:0.000000:0.000000
iv) :@0.404242:0.542281:0.427129:0.542281:0.427129:0.525567:0.404242:0.525567:0.000000:0.000000:0.000000:0.000000
Si   ≠ 0, :@0.427977:0.542065:0.487391:0.542065:0.487391:0.525567:0.427977:0.525567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.443928:0.542180:0.452906:0.542180:0.452906:0.525711:0.443928:0.525711:0.000000
1:@0.498219:0.535273:0.506345:0.535273:0.506345:0.519493:0.498219:0.519493:0.000000
a:@0.494128:0.551980:0.502715:0.551980:0.502715:0.536228:0.494128:0.536228:0.000000
 = :@0.515549:0.542063:0.534641:0.542063:0.534641:0.525566:0.515549:0.525566:0.000000:0.000000:0.000000
1:@0.542015:0.533534:0.550511:0.533534:0.550511:0.517036:0.542015:0.517036:0.000000
| |:@0.536351:0.551296:0.555782:0.551296:0.555782:0.534081:0.536351:0.534081:0.000000:0.000000:0.000000
a:@0.541577:0.551252:0.550555:0.551252:0.550555:0.534783:0.541577:0.534783:0.000000
.:@0.557882:0.542063:0.560637:0.542063:0.560637:0.525566:0.557882:0.525566:0.000000
v) :@0.404242:0.573887:0.422949:0.573887:0.422949:0.557173:0.404242:0.557173:0.000000:0.000000:0.000000
a:@0.427977:0.573786:0.436954:0.573786:0.436954:0.557318:0.427977:0.557318:0.000000
 ≤ | |, y, –  ≤ | |.:@0.436954:0.573671:0.556206:0.573671:0.556206:0.557173:0.436954:0.557173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.461055:0.573786:0.470033:0.573786:0.470033:0.557318:0.461055:0.557318:0.000000
a:@0.506386:0.573786:0.515364:0.573786:0.515364:0.557318:0.506386:0.557318:0.000000
a:@0.539465:0.573786:0.548442:0.573786:0.548442:0.557318:0.539465:0.557318:0.000000
vi) :@0.404242:0.598367:0.427187:0.598367:0.427187:0.581652:0.404242:0.581652:0.000000:0.000000:0.000000:0.000000
|:@0.427977:0.598150:0.432986:0.598150:0.432986:0.581652:0.427977:0.581652:0.000000
a + b:@0.432986:0.598265:0.470399:0.598265:0.470399:0.581797:0.432986:0.581797:0.000000:0.000000:0.000000:0.000000:0.000000
| ≤ | | + | |. :@0.470399:0.598150:0.558769:0.598150:0.558769:0.581652:0.470399:0.581652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.499509:0.598265:0.508486:0.598265:0.508486:0.581797:0.499509:0.581797:0.000000
b:@0.537596:0.598265:0.546863:0.598265:0.546863:0.581797:0.537596:0.581797:0.000000
(desigualdad triangular):@0.585162:0.598150:0.753772:0.598150:0.753772:0.581652:0.585162:0.581652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vii) :@0.404242:0.622846:0.431445:0.622846:0.431445:0.606131:0.404242:0.606131:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.427977:0.622629:0.432119:0.622629:0.432119:0.606131:0.427977:0.606131:0.000000
a:@0.443743:0.622412:0.451940:0.622412:0.451940:0.607376:0.443743:0.607376:0.000000
2:@0.451939:0.616568:0.456235:0.616568:0.456235:0.607801:0.451939:0.607801:0.000000
 = | |.:@0.461905:0.622627:0.502747:0.622627:0.502747:0.606130:0.461905:0.606130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.486005:0.622743:0.494983:0.622743:0.494983:0.606274:0.486005:0.606274:0.000000
En muchos cálculos, aparece el valor absoluto de productos o cocien-:@0.404244:0.660944:0.891707:0.660944:0.891707:0.644446:0.404244:0.644446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tes de números reales. En tal caso, se debe determinar las condiciones :@0.404244:0.678294:0.895926:0.678294:0.895926:0.661797:0.404244:0.661797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que han de verificar cada uno de los términos que figuran en el valor :@0.404244:0.695645:0.895962:0.695645:0.895962:0.679147:0.404244:0.679147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
absoluto para precisar cuándo son positivos, y cuándo son negativos :@0.404244:0.712996:0.895924:0.712996:0.895924:0.696498:0.404244:0.696498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y, con esta información, decidir el signo de todo el término que se :@0.404244:0.730347:0.895966:0.730347:0.895966:0.713849:0.404244:0.713849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encuentra en el interior del valor absoluto.:@0.404244:0.747697:0.703660:0.747697:0.703660:0.731200:0.404244:0.731200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.404244:0.779261:0.522222:0.779261:0.522222:0.762474:0.404244:0.762474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  :@0.404244:0.803581:0.424684:0.803581:0.424684:0.786867:0.404244:0.786867:0.000000:0.000000:0.000000:0.000000
Para todo       , | | = | |. En efecto, como –1     = –  se sigue :@0.427979:0.803364:0.895615:0.803351:0.895615:0.786853:0.427979:0.786867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.501726:0.803480:0.509201:0.803480:0.509201:0.787011:0.501726:0.787011:0.000000
:@0.513343:0.803148:0.529391:0.803148:0.529391:0.788501:0.513343:0.788501:0.000000
R:@0.533533:0.802396:0.547442:0.802396:0.547442:0.788949:0.533533:0.788949:0.000000
–x:@0.563490:0.803480:0.581002:0.803480:0.581002:0.787011:0.563490:0.787011:0.000000:0.000000
x:@0.610112:0.803480:0.617587:0.803480:0.617587:0.787011:0.610112:0.787011:0.000000
×:@0.771723:0.801612:0.781122:0.801612:0.781122:0.787267:0.771723:0.787267:0.000000
x:@0.785264:0.803466:0.792739:0.803466:0.792739:0.786997:0.785264:0.786997:0.000000
x,:@0.822330:0.803466:0.832772:0.803466:0.832772:0.786997:0.822330:0.786997:0.000000:0.000000
que | | = |–1|   | | = |–1| | | = | |. Nótese que hemos utilizado :@0.427989:0.820701:0.887408:0.820701:0.887408:0.804204:0.427989:0.804204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–x:@0.464150:0.820817:0.481662:0.820817:0.481662:0.804348:0.464150:0.804348:0.000000:0.000000
×:@0.538907:0.818963:0.548305:0.818963:0.548305:0.804617:0.538907:0.804617:0.000000
x:@0.557456:0.820817:0.564931:0.820817:0.564931:0.804348:0.557456:0.804348:0.000000
x:@0.627196:0.820817:0.634671:0.820817:0.634671:0.804348:0.627196:0.804348:0.000000
x:@0.663781:0.820817:0.671256:0.820817:0.671256:0.804348:0.663781:0.804348:0.000000
la propiedad | | = | || |, :@0.427974:0.838052:0.614231:0.838052:0.614231:0.821554:0.427974:0.821554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ab:@0.526824:0.838168:0.544953:0.838168:0.544953:0.821699:0.526824:0.821699:0.000000:0.000000
a b:@0.574063:0.838168:0.602325:0.838168:0.602325:0.821699:0.574063:0.821699:0.000000:0.000000:0.000000
a, b:@0.625403:0.838168:0.650332:0.838168:0.650332:0.821699:0.625403:0.821699:0.000000:0.000000:0.000000:0.000000
 :@0.650332:0.838052:0.654474:0.838052:0.654474:0.821554:0.650332:0.821554:0.000000
 :@0.654474:0.837835:0.675339:0.837835:0.675339:0.823188:0.654474:0.823188:0.000000:0.000000
R:@0.675339:0.837083:0.689248:0.837083:0.689248:0.823637:0.675339:0.823637:0.000000
  y  |–1| = 1.:@0.689248:0.838052:0.772994:0.838052:0.772994:0.821554:0.689248:0.821554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.  :@0.404238:0.869876:0.424678:0.869876:0.424678:0.853162:0.404238:0.853162:0.000000:0.000000:0.000000:0.000000
Supón que   < –2. Sumando –3 en ambos miembros, obtenemos  :@0.427973:0.869659:0.890551:0.869659:0.890551:0.853162:0.427973:0.853162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.508018:0.869775:0.515493:0.869775:0.515493:0.853306:0.508018:0.853306:0.000000
x:@0.427973:0.887126:0.435448:0.887126:0.435448:0.870657:0.427973:0.870657:0.000000
 – 3 < –5 y, en consecuencia, | – 3 = –( – 3) = 3 :@0.435448:0.887010:0.796380:0.887010:0.796380:0.870512:0.435448:0.870512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.648808:0.887126:0.660425:0.887126:0.660425:0.870657:0.648808:0.870657:0.000000:0.000000
| :@0.683563:0.887126:0.692541:0.887126:0.692541:0.870657:0.683563:0.870657:0.000000:0.000000
x :@0.723943:0.887126:0.735560:0.887126:0.735560:0.870657:0.723943:0.870657:0.000000:0.000000
– x:@0.796380:0.887126:0.818034:0.887126:0.818034:0.870657:0.796380:0.870657:0.000000:0.000000:0.000000
. Nótese :@0.818034:0.887010:0.880030:0.887010:0.880030:0.870512:0.818034:0.870512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que   – 3 es negativo. Si   > 10, entonces   + 1 > 11. Luego,  :@0.427973:0.904361:0.852092:0.904361:0.852092:0.887863:0.427973:0.887863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.459123:0.904477:0.466598:0.904477:0.466598:0.888008:0.459123:0.888008:0.000000
x:@0.600489:0.904477:0.607964:0.904477:0.607964:0.888008:0.600489:0.888008:0.000000
x:@0.719797:0.904477:0.727272:0.904477:0.727272:0.888008:0.719797:0.888008:0.000000
|  + 1| =   + 1. Observa que   + 1 es positivo.:@0.427973:0.921712:0.750448:0.921712:0.750448:0.905214:0.427973:0.905214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.437124:0.921827:0.448741:0.921827:0.448741:0.905359:0.437124:0.905359:0.000000:0.000000
x:@0.496287:0.921827:0.503762:0.921827:0.503762:0.905359:0.496287:0.905359:0.000000
x:@0.633375:0.921827:0.640850:0.921827:0.640850:0.905359:0.633375:0.905359:0.000000
Saberes previos:@0.199646:0.101454:0.307805:0.101454:0.307805:0.085981:0.199646:0.085981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la vida cotidiana, ¿qué :@0.199884:0.130082:0.365281:0.130082:0.365281:0.115019:0.199884:0.115019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entiendes por intervalo?:@0.153341:0.145924:0.309470:0.145924:0.309470:0.130861:0.153341:0.130861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.189511:0.363493:0.189511:0.363493:0.174039:0.199646:0.174039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué signo adquiere el :@0.199884:0.218139:0.350261:0.218139:0.350261:0.203075:0.199884:0.203075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valor absoluto de un número :@0.153341:0.233981:0.346986:0.233981:0.346986:0.218917:0.153341:0.218917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
negativo? ¿Por qué?:@0.153341:0.249823:0.279039:0.249823:0.279039:0.234759:0.153341:0.234759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.530545:0.297267:0.530545:0.297267:0.515073:0.199644:0.515073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.543113:0.283707:0.543113:0.283707:0.527641:0.199644:0.527641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para comprender mejor :@0.199880:0.567588:0.358085:0.567588:0.358085:0.552525:0.199880:0.552525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la resolución de las ecuaciones  :@0.153337:0.583430:0.353453:0.583430:0.353453:0.568367:0.153337:0.568367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e inecuaciones, es preciso recor-:@0.153337:0.599272:0.360178:0.599272:0.360178:0.584209:0.153337:0.584209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dar las propiedades de orden :@0.153337:0.615114:0.345594:0.615114:0.345594:0.600051:0.153337:0.600051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los números reales,  :@0.153337:0.630956:0.303113:0.630956:0.303113:0.615893:0.153337:0.615893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los intervalos y las propiedades :@0.153337:0.646798:0.357519:0.646798:0.357519:0.631735:0.153337:0.631735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del valor absoluto.:@0.153337:0.662640:0.271699:0.662640:0.271699:0.647577:0.153337:0.647577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Escribe:@0.153344:0.850905:0.203720:0.850905:0.203720:0.835433:0.153344:0.835433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en el cuaderno un :@0.203720:0.850483:0.328785:0.850483:0.328785:0.835420:0.203720:0.835420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejemplo de ecuación y otro de :@0.153344:0.866325:0.355115:0.866325:0.355115:0.851262:0.153344:0.851262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inecuación de primer grado. :@0.153344:0.882167:0.339496:0.882167:0.339496:0.867104:0.153344:0.867104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Luego, :@0.153344:0.898009:0.199096:0.898009:0.199096:0.882946:0.153344:0.882946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
identifica:@0.199096:0.898431:0.265408:0.898431:0.265408:0.882959:0.199096:0.882959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 sus elementos :@0.265410:0.898009:0.364227:0.898009:0.364227:0.882946:0.265410:0.882946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y :@0.153344:0.913851:0.164267:0.913851:0.164267:0.898788:0.153344:0.898788:0.000000:0.000000
resuélvelas:@0.164267:0.914273:0.240466:0.914273:0.240466:0.898801:0.164267:0.898801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.240467:0.913851:0.242983:0.913851:0.242983:0.898788:0.240467:0.898788:0.000000
Pixabay.com:@0.138570:0.820979:0.138570:0.786610:0.127101:0.786610:0.127101:0.820979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.301293:0.297267:0.301293:0.297267:0.285820:0.199644:0.285820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199644:0.313861:0.311603:0.313861:0.311603:0.298388:0.199644:0.298388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende esta simbología::@0.193071:0.338335:0.357340:0.338335:0.357340:0.323272:0.193071:0.323272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
|x|  valor absoluto:@0.153335:0.357742:0.269972:0.357742:0.269972:0.342679:0.153335:0.342679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≥  mayor o igual que:@0.153335:0.377148:0.287299:0.377148:0.287299:0.362085:0.153335:0.362085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≤  menor o igual que:@0.153335:0.396555:0.289393:0.396555:0.289393:0.381492:0.153335:0.381492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≠  no es igual:@0.153335:0.415961:0.239209:0.415961:0.239209:0.400898:0.153335:0.400898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⇔:@0.153335:0.434905:0.171663:0.434905:0.171663:0.418733:0.153335:0.418733:0.000000
  si solamente si:@0.171663:0.435367:0.272752:0.435367:0.272752:0.420304:0.171663:0.420304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.153344:0.456383:0.174208:0.456383:0.174208:0.441736:0.153344:0.441736:0.000000:0.000000
 pertenece a:@0.174207:0.456279:0.254082:0.456279:0.254082:0.441216:0.174207:0.441216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000