46:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Sistemas de ecuaciones:@0.073089:0.043661:0.282490:0.043661:0.282490:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 1. Ecuaciones e inecuaciones de primer grado en :@0.073089:0.101435:0.882965:0.101435:0.882965:0.070193:0.073089:0.070193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.882965:0.102494:0.907128:0.102494:0.907128:0.070395:0.882965:0.070395:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una ecuación es una igualdad entre dos expresiones que contiene una o más variables.:@0.293660:0.235115:0.927442:0.235115:0.927442:0.218681:0.293660:0.218681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En cambio, una inecuación es una desigualdad entre dos expresiones algebraicas de una :@0.293660:0.251757:0.931076:0.251757:0.931076:0.235323:0.293660:0.235323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o varias incógnitas que se verifica para ciertos valores de las incógnitas; se expresa con :@0.293660:0.268399:0.930444:0.268399:0.930444:0.251965:0.293660:0.251965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los signos >, <, ≥ y ≤.:@0.293660:0.285041:0.445476:0.285041:0.445476:0.268607:0.293660:0.268607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.1 Ecuaciones de primer grado:@0.293660:0.312403:0.540570:0.312403:0.540570:0.295456:0.293660:0.295456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En un salón de clases, la cuarta parte son niñas y los niños exceden a la mitad en tres. :@0.293660:0.336186:0.931149:0.336186:0.931149:0.319753:0.293660:0.319753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuántos estudiantes tiene el salón de clases? :@0.293660:0.352828:0.628807:0.352828:0.628807:0.336395:0.293660:0.336395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Traducimos del lenguaje cotidiano al lenguaje matemático: la variable   representa el :@0.293660:0.380190:0.930976:0.380190:0.930976:0.363756:0.293660:0.363756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.818359:0.380190:0.825814:0.380190:0.825814:0.363784:0.818359:0.363784:0.000000
número de estudiantes en el salón de clases.:@0.293642:0.396832:0.616466:0.396832:0.616466:0.380398:0.293642:0.380398:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La cuarta parte: —. La mitad excedida en 3: — + 3.:@0.293642:0.429270:0.659302:0.429270:0.659302:0.412836:0.293642:0.412836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.405447:0.429270:0.408797:0.429270:0.408797:0.412586:0.405447:0.412586:0.000000
x:@0.414485:0.420727:0.421940:0.420727:0.421940:0.404321:0.414485:0.404321:0.000000
4:@0.413712:0.437535:0.422695:0.437535:0.422695:0.421101:0.413712:0.421101:0.000000
x:@0.615235:0.420727:0.622690:0.420727:0.622690:0.404321:0.615235:0.404321:0.000000
2:@0.614462:0.437535:0.623444:0.437535:0.623444:0.421101:0.614462:0.421101:0.000000
Entonces, la ecuación buscada es:  :@0.293642:0.465452:0.545972:0.465452:0.545972:0.449018:0.293642:0.449018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.551029:0.457209:0.558484:0.457209:0.558484:0.441774:0.551029:0.441774:0.000000
4:@0.550292:0.476597:0.559275:0.476597:0.559275:0.460884:0.550292:0.460884:0.000000
+:@0.563526:0.466792:0.573631:0.466792:0.573631:0.451177:0.563526:0.451177:0.000000
x:@0.588523:0.457209:0.595978:0.457209:0.595978:0.441774:0.588523:0.441774:0.000000
2:@0.587786:0.476597:0.596769:0.476597:0.596769:0.460884:0.587786:0.460884:0.000000
+:@0.601021:0.466792:0.611127:0.466792:0.611127:0.451177:0.601021:0.451177:0.000000
3:@0.613575:0.466113:0.622558:0.466113:0.622558:0.450400:0.613575:0.450400:0.000000
=:@0.634437:0.466792:0.644543:0.466792:0.644543:0.451177:0.634437:0.451177:0.000000
x:@0.649181:0.466113:0.656636:0.466113:0.656636:0.450677:0.649181:0.450677:0.000000
.:@0.660868:0.465470:0.664071:0.465470:0.664071:0.449036:0.660868:0.449036:0.000000
Definición de ecuación lineal. :@0.303983:0.512683:0.526601:0.512683:0.526601:0.496014:0.303983:0.496014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Es una expresión de la forma   +  =  , donde  ,   y   :@0.526413:0.512683:0.914604:0.512683:0.914604:0.496249:0.526413:0.496249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax b  c:@0.734745:0.512683:0.804068:0.512683:0.804068:0.496277:0.734745:0.496277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.862290:0.512683:0.910573:0.512683:0.910573:0.496277:0.862290:0.496277:0.000000:0.000000:0.000000:0.000000:0.000000
son números reales y el grado de la incógnita  es 1.  :@0.303998:0.529325:0.680408:0.529325:0.680408:0.512891:0.303998:0.512891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.627156:0.529325:0.630506:0.529325:0.630506:0.512642:0.627156:0.512642:0.000000
x:@0.630322:0.529325:0.637777:0.529325:0.637777:0.512919:0.630322:0.512919:0.000000
Resolverla significa encontrar el valor de la variable que satisface la igualdad.:@0.303998:0.545967:0.860683:0.545967:0.860683:0.529533:0.303998:0.529533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda:@0.293672:0.171678:0.365571:0.171678:0.365571:0.155009:0.293672:0.155009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. En lenguaje algebraico, la expresión “parte de” se refiere a una di-:@0.365571:0.171678:0.848651:0.171678:0.848651:0.155244:0.365571:0.155244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
visión y la palabra “veces”, a una multiplicación. :@0.293672:0.188320:0.638530:0.188320:0.638530:0.171886:0.293672:0.171886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Escribe:@0.638530:0.188320:0.693218:0.188320:0.693218:0.171650:0.638530:0.171650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.693218:0.188320:0.697028:0.188320:0.697028:0.171373:0.693218:0.171373:0.000000
un ejemplo.:@0.697028:0.188320:0.784299:0.188320:0.784299:0.171886:0.697028:0.171886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El símbolo ∞ significa :@0.080953:0.674857:0.226987:0.674857:0.226987:0.659917:0.080953:0.659917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
infinito, es decir, no  :@0.080953:0.689986:0.216177:0.689986:0.216177:0.675046:0.080953:0.675046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiene fin.:@0.080953:0.705115:0.138249:0.705115:0.138249:0.690175:0.080953:0.690175:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+∞: significa más infinito.:@0.080953:0.727392:0.247821:0.727392:0.247821:0.712452:0.080953:0.712452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–∞: significa menos :@0.080953:0.749669:0.215208:0.749669:0.215208:0.734729:0.080953:0.734729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
infinito.:@0.080953:0.764798:0.130351:0.764798:0.130351:0.749858:0.080953:0.749858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.634150:0.187141:0.634150:0.187141:0.617203:0.078581:0.617203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.650792:0.176057:0.650792:0.176057:0.633845:0.078581:0.633845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una inecuación es una :@0.080204:0.286865:0.235076:0.286865:0.235076:0.271925:0.080204:0.271925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desigualdad de dos :@0.080204:0.301994:0.214560:0.301994:0.214560:0.287054:0.080204:0.287054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cantidades, tal que la una :@0.080204:0.317123:0.253097:0.317123:0.253097:0.302183:0.080204:0.302183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es mayor que la otra. Los :@0.080204:0.332252:0.247924:0.332252:0.247924:0.317312:0.080204:0.317312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
símbolos <, >, ≥ y ≤ se :@0.080204:0.347381:0.233570:0.347381:0.233570:0.332441:0.080204:0.332441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denominan signos de la :@0.080204:0.362510:0.243876:0.362510:0.243876:0.347570:0.080204:0.347570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desigualdad.:@0.080204:0.377639:0.164825:0.377639:0.164825:0.362699:0.080204:0.362699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.246158:0.187141:0.246158:0.187141:0.229211:0.078581:0.229211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.262800:0.176056:0.262800:0.176056:0.245853:0.078581:0.245853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A continuación, resolveremos la ecuación planteada anteriormente.:@0.293660:0.577303:0.783525:0.577303:0.783525:0.560869:0.293660:0.560869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Primero, eliminamos paréntesis.:@0.293660:0.597519:0.522799:0.597519:0.522799:0.581085:0.293660:0.581085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.304331:0.628116:0.311786:0.628116:0.311786:0.612680:0.304331:0.612680:0.000000
4:@0.303600:0.647500:0.312583:0.647500:0.312583:0.631787:0.303600:0.631787:0.000000
+:@0.316830:0.637699:0.326935:0.637699:0.326935:0.622083:0.316830:0.622083:0.000000
x:@0.332310:0.628116:0.339765:0.628116:0.339765:0.612680:0.332310:0.612680:0.000000
+:@0.343336:0.628795:0.353442:0.628795:0.353442:0.613180:0.343336:0.613180:0.000000
6:@0.356258:0.628116:0.365241:0.628116:0.365241:0.612403:0.356258:0.612403:0.000000
2:@0.343708:0.647500:0.352691:0.647500:0.352691:0.631787:0.343708:0.631787:0.000000
=:@0.369854:0.637699:0.379960:0.637699:0.379960:0.622083:0.369854:0.622083:0.000000
x:@0.384599:0.637019:0.392054:0.637019:0.392054:0.621584:0.384599:0.621584:0.000000
Luego, resolvemos la suma de fracciones y eliminamos el deno-:@0.444400:0.630070:0.918755:0.630070:0.918755:0.613636:0.444400:0.613636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
minador aplicando la propiedad del inverso multiplicativo.:@0.444400:0.646712:0.877232:0.646712:0.877232:0.630278:0.444400:0.630278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.303821:0.673306:0.311276:0.673306:0.311276:0.657871:0.303821:0.657871:0.000000
+:@0.314847:0.673985:0.324952:0.673985:0.324952:0.658370:0.314847:0.658370:0.000000
2:@0.328137:0.673306:0.337120:0.673306:0.337120:0.657593:0.328137:0.657593:0.000000
x:@0.339119:0.673306:0.346574:0.673306:0.346574:0.657871:0.339119:0.657871:0.000000
+:@0.350145:0.673985:0.360251:0.673985:0.360251:0.658370:0.350145:0.658370:0.000000
12:@0.362702:0.673306:0.380465:0.673306:0.380465:0.657593:0.362702:0.657593:0.000000:0.000000
4:@0.332739:0.692690:0.341721:0.692690:0.341721:0.676977:0.332739:0.676977:0.000000
=:@0.385450:0.682889:0.395556:0.682889:0.395556:0.667273:0.385450:0.667273:0.000000
x:@0.400195:0.682209:0.407650:0.682209:0.407650:0.666774:0.400195:0.666774:0.000000
3:@0.302743:0.710025:0.311726:0.710025:0.311726:0.694312:0.302743:0.694312:0.000000
x:@0.313364:0.710025:0.320819:0.710025:0.320819:0.694590:0.313364:0.694590:0.000000
+:@0.324390:0.710705:0.334496:0.710705:0.334496:0.695089:0.324390:0.695089:0.000000
12 4:@0.336944:0.710025:0.380496:0.710025:0.380496:0.694312:0.336944:0.694312:0.000000:0.000000:0.000000:0.000000
=:@0.358223:0.710705:0.368328:0.710705:0.368328:0.695089:0.358223:0.695089:0.000000
x:@0.382134:0.710025:0.389589:0.710025:0.389589:0.694590:0.382134:0.694590:0.000000
Después, transponemos los términos agrupando las variables en :@0.444400:0.685543:0.922503:0.685543:0.922503:0.669109:0.444400:0.669109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la izquierda y las constantes (números) en la derecha.:@0.444400:0.702185:0.838279:0.702185:0.838279:0.685751:0.444400:0.685751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3– 4:@0.301400:0.737335:0.343230:0.737335:0.343230:0.721041:0.301400:0.721041:0.000000:0.000000:0.000000:0.000000
–12:@0.370350:0.737335:0.397088:0.737335:0.397088:0.721041:0.370350:0.721041:0.000000:0.000000:0.000000
–:@0.301763:0.757961:0.310888:0.757961:0.310888:0.741667:0.301763:0.741667:0.000000
–12:@0.337789:0.757961:0.364527:0.757961:0.364527:0.741667:0.337789:0.741667:0.000000:0.000000:0.000000
12:@0.326494:0.778575:0.344106:0.778575:0.344106:0.762281:0.326494:0.762281:0.000000:0.000000
x:@0.311145:0.737338:0.318536:0.737338:0.318536:0.721072:0.311145:0.721072:0.000000
x:@0.345219:0.737338:0.352610:0.737338:0.352610:0.721072:0.345219:0.721072:0.000000
x:@0.312650:0.757961:0.320041:0.757961:0.320041:0.741694:0.312650:0.741694:0.000000
x:@0.302850:0.778575:0.310242:0.778575:0.310242:0.762309:0.302850:0.762309:0.000000
:@0.355777:0.738383:0.370980:0.738383:0.370980:0.720879:0.355777:0.720879:0.000000
:@0.321642:0.759011:0.336845:0.759011:0.336845:0.741507:0.321642:0.741507:0.000000
:@0.312472:0.779627:0.327675:0.779627:0.327675:0.762123:0.312472:0.762123:0.000000
Finalmente, despejamos la variable x y multiplicamos los dos :@0.444400:0.751101:0.922862:0.751101:0.922862:0.734668:0.444400:0.734668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
miembros de la igualdad por (–1).:@0.444400:0.767743:0.689175:0.767743:0.689175:0.751309:0.444400:0.751309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.2 Propiedades de las ecuaciones:@0.293663:0.817253:0.560950:0.817253:0.560950:0.800306:0.293663:0.800306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedad:@0.351745:0.850569:0.437173:0.850569:0.437173:0.833386:0.351745:0.833386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Enunciado:@0.667270:0.850569:0.754061:0.850569:0.754061:0.833386:0.667270:0.833386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   =  , entonces  :@0.300985:0.875266:0.438282:0.875266:0.438282:0.858832:0.300985:0.858832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.317404:0.875266:0.326663:0.875266:0.326663:0.858860:0.317404:0.858860:0.000000
b:@0.345696:0.875266:0.354955:0.875266:0.354955:0.858860:0.345696:0.858860:0.000000
a:@0.300985:0.891908:0.310243:0.891908:0.310243:0.875502:0.300985:0.875502:0.000000
 ±   =   ±  .:@0.310243:0.891908:0.395119:0.891908:0.395119:0.875474:0.310243:0.875474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.329276:0.891908:0.336934:0.891908:0.336934:0.875502:0.329276:0.875502:0.000000
b:@0.355967:0.891908:0.365226:0.891908:0.365226:0.875502:0.355967:0.875502:0.000000
c:@0.384259:0.891908:0.391916:0.891908:0.391916:0.875502:0.384259:0.875502:0.000000
Una igualdad no cambia si se le suma o se le resta un :@0.502157:0.875266:0.894779:0.875266:0.894779:0.858832:0.502157:0.858832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mismo número a cada miembro.:@0.502157:0.891908:0.741871:0.891908:0.741871:0.875474:0.502157:0.875474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   =   y   ≠ 0, entonces   Una igualdad se mantiene si se multiplica o divide por :@0.300985:0.916607:0.902257:0.916607:0.902257:0.900173:0.300985:0.900173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.317404:0.916607:0.326663:0.916607:0.326663:0.900201:0.317404:0.900201:0.000000
b c:@0.345696:0.916607:0.378774:0.916607:0.378774:0.900201:0.345696:0.900201:0.000000:0.000000:0.000000
ac:@0.300985:0.933249:0.317901:0.933249:0.317901:0.916843:0.300985:0.916843:0.000000:0.000000
 =  .:@0.317901:0.933249:0.357053:0.933249:0.357053:0.916815:0.317901:0.916815:0.000000:0.000000:0.000000:0.000000:0.000000
bc:@0.336934:0.933249:0.353850:0.933249:0.353850:0.916843:0.336934:0.916843:0.000000:0.000000
un mismo número distinto de cero en cada miembro.:@0.502157:0.933249:0.894668:0.933249:0.894668:0.916815:0.502157:0.916815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000