42:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 Números naturales:@0.073089:0.043661:0.242487:0.043661:0.242487:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8.1 ¿Qué es una ecuación?:@0.293660:0.231730:0.498971:0.231730:0.498971:0.214783:0.293660:0.214783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El número 32 puede escribirse de la forma 6 4, es decir, 6 4 32. El valor de en :@0.293660:0.259092:0.930951:0.259093:0.930951:0.242659:0.293660:0.242658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.617775:0.259092:0.625230:0.259092:0.625230:0.242686:0.617775:0.242686:0.000000 2:@0.627516:0.258538:0.642849:0.258538:0.642849:0.244823:0.627516:0.244823:0.000000 x:@0.734079:0.259093:0.741534:0.259093:0.741534:0.242687:0.734079:0.242687:0.000000 2 5:@0.743820:0.258538:0.788034:0.258538:0.788034:0.244823:0.743820:0.244823:0.000000:0.000000:0.000000 x:@0.896253:0.259093:0.903708:0.259093:0.903708:0.242687:0.896253:0.242687:0.000000 este caso es 6, pues 6 6 4 32.:@0.293660:0.275735:0.546134:0.275735:0.546134:0.259301:0.293660:0.259301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3 2 5:@0.450477:0.275180:0.522978:0.275180:0.522978:0.261465:0.450477:0.261465:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.465718:0.275735:0.469749:0.275735:0.469749:0.259301:0.465718:0.259301:0.000000 Lo que hicimos fue expresar el número 32 como el producto de un número desconocido :@0.293660:0.303098:0.930776:0.303098:0.930776:0.286664:0.293660:0.286664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (notado con la letra ) por 6 y a este producto le restamos 4.:@0.293660:0.319740:0.726232:0.319740:0.726232:0.303306:0.293660:0.303306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.438912:0.319740:0.446367:0.319740:0.446367:0.303334:0.438912:0.303334:0.000000 La expresión 6 4 32 es lo que conocemos con el nombre de ecuación, en donde x :@0.293660:0.347102:0.931149:0.347103:0.931149:0.330669:0.293660:0.330668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.398802:0.347102:0.406257:0.347102:0.406257:0.330696:0.398802:0.330696:0.000000 2:@0.408461:0.346549:0.423794:0.346549:0.423794:0.332833:0.408461:0.332833:0.000000 =:@0.437136:0.347103:0.448107:0.347103:0.448107:0.330669:0.437136:0.330669:0.000000 representa un valor desconocido y la llamamos :@0.293660:0.363745:0.639188:0.363745:0.639188:0.347311:0.293660:0.347311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 incógnita:@0.638815:0.363745:0.710651:0.363745:0.710651:0.347076:0.638815:0.347076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . :@0.710548:0.363745:0.717782:0.363745:0.717782:0.347311:0.710548:0.347311:0.000000:0.000000 Las ecuaciones están conformadas por :@0.293679:0.391107:0.578941:0.391107:0.578941:0.374673:0.293679:0.374673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 términos variables y constantes.:@0.578623:0.391107:0.820463:0.391107:0.820463:0.374437:0.578623:0.374437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6:@0.474386:0.418472:0.483829:0.418472:0.483829:0.401802:0.474386:0.401802:0.000000 x:@0.483755:0.418472:0.491873:0.418472:0.491873:0.401788:0.483755:0.401788:0.000000 4 32:@0.491801:0.418472:0.557967:0.418472:0.557967:0.402038:0.491801:0.402038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.494021:0.417917:0.537938:0.417917:0.537938:0.404201:0.494021:0.404201:0.000000:0.000000:0.000000 :@0.293660:0.445835:0.297691:0.445835:0.297691:0.429401:0.293660:0.429401:0.000000 :@0.353902:0.445835:0.357933:0.445835:0.357933:0.429401:0.353902:0.429401:0.000000 :@0.414145:0.445835:0.418176:0.445835:0.418176:0.429401:0.414145:0.429401:0.000000 :@0.474386:0.445835:0.478417:0.445835:0.478417:0.429401:0.474386:0.429401:0.000000 :@0.534628:0.445835:0.538659:0.445835:0.538659:0.429401:0.534628:0.429401:0.000000 Términos constantes (su valor no cambia):@0.594876:0.445835:0.895307:0.445835:0.895307:0.429401:0.594876:0.429401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Término variable (su valor depende del valor que tome ):@0.293660:0.473198:0.706535:0.473198:0.706535:0.456764:0.293660:0.456764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.694276:0.473198:0.701731:0.473198:0.701731:0.456792:0.694276:0.456792:0.000000 Al número que, al ser reemplazado por hace que la igualdad se cumpla, se le llama :@0.293642:0.500560:0.930993:0.500560:0.930993:0.484126:0.293642:0.484126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.589943:0.500560:0.597398:0.500560:0.597398:0.484154:0.589943:0.484154:0.000000 solución de la ecuación.:@0.293642:0.517202:0.474401:0.517202:0.474401:0.500532:0.293642:0.500532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Entonces, la solución de la ecuación 6 4 32 es 6. Veamos por qué::@0.293642:0.544564:0.801530:0.544566:0.801530:0.528132:0.293642:0.528130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.566934:0.544564:0.574389:0.544564:0.574389:0.528158:0.566934:0.528158:0.000000 2 5:@0.576553:0.544011:0.620471:0.544011:0.620471:0.530296:0.576553:0.530296:0.000000:0.000000:0.000000 6 6 4 32:@0.561522:0.571929:0.665165:0.571929:0.665165:0.555496:0.561522:0.555496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3 2 5:@0.572637:0.571375:0.645138:0.571375:0.645138:0.557659:0.572637:0.557659:0.000000:0.000000:0.000000:0.000000:0.000000 36 4 32:@0.581200:0.599291:0.665165:0.599291:0.665165:0.582858:0.581200:0.582858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.601222:0.598737:0.645138:0.598737:0.645138:0.585021:0.601222:0.585021:0.000000:0.000000:0.000000 32 32:@0.609786:0.626655:0.665165:0.626655:0.665165:0.610221:0.609786:0.610221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.629805:0.626100:0.645138:0.626100:0.645138:0.612384:0.629805:0.612384:0.000000 8.2 Propiedades de la igualdad:@0.293660:0.654018:0.535399:0.654018:0.535399:0.637071:0.293660:0.637071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Propiedad aditiva de la igualdad.:@0.293660:0.678880:0.559710:0.678880:0.559710:0.662446:0.293660:0.662446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si, , entonces, a :@0.323788:0.703745:0.530933:0.703742:0.530933:0.687308:0.323788:0.687312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.343079:0.703745:0.352337:0.703745:0.352337:0.687339:0.343079:0.687339:0.000000 5:@0.354493:0.703187:0.369826:0.703187:0.369826:0.689471:0.354493:0.689471:0.000000 b:@0.371955:0.703742:0.381213:0.703742:0.381213:0.687335:0.371955:0.687335:0.000000 1 5 1 :@0.472975:0.703187:0.548965:0.703187:0.548965:0.689471:0.472975:0.689471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.490437:0.703742:0.498094:0.703742:0.498094:0.687335:0.490437:0.687335:0.000000 b:@0.517710:0.703742:0.526969:0.703742:0.526969:0.687335:0.517710:0.687335:0.000000 c, y, a:@0.548873:0.703742:0.585279:0.703742:0.585279:0.687335:0.548873:0.687335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.585243:0.703742:0.672761:0.703742:0.672761:0.687308:0.585243:0.687308:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5 2:@0.587463:0.703187:0.658944:0.703187:0.658944:0.689471:0.587463:0.689471:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.604925:0.703742:0.612583:0.703742:0.612583:0.687335:0.604925:0.687335:0.000000 b:@0.632198:0.703742:0.641457:0.703742:0.641457:0.687335:0.632198:0.687335:0.000000 c:@0.661072:0.703742:0.668730:0.703742:0.668730:0.687335:0.661072:0.687335:0.000000 Ejemplo::@0.323778:0.728607:0.390099:0.728607:0.390099:0.711938:0.323778:0.711938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8 7 1 entonces 8 5 (7 1) 5 :@0.389989:0.728607:0.675641:0.728602:0.675641:0.712168:0.389989:0.712173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 1:@0.406794:0.728053:0.450714:0.728047:0.450714:0.714332:0.406794:0.714337:0.000000:0.000000:0.000000 1 5:@0.548155:0.728047:0.592074:0.728047:0.592074:0.714332:0.548155:0.714332:0.000000:0.000000:0.000000 1 1:@0.611851:0.728047:0.660565:0.728047:0.660565:0.714332:0.611851:0.714332:0.000000:0.000000:0.000000 8 3 (7 1) 3:@0.701245:0.728602:0.834171:0.728602:0.834171:0.712168:0.701245:0.712168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5 1 2:@0.712373:0.728047:0.823053:0.728047:0.823053:0.714332:0.712373:0.714332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 13 8 5 :@0.593521:0.753464:0.672543:0.753464:0.672543:0.737030:0.593521:0.737030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 1:@0.613551:0.752909:0.657468:0.752909:0.657468:0.739194:0.613551:0.739194:0.000000:0.000000:0.000000 5 8 3:@0.768022:0.753464:0.834171:0.753464:0.834171:0.737030:0.768022:0.737030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 2:@0.779136:0.752909:0.823053:0.752909:0.823053:0.739194:0.779136:0.739194:0.000000:0.000000:0.000000 13 13 :@0.613217:0.778326:0.672552:0.778326:0.672552:0.761892:0.613217:0.761892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.633232:0.777771:0.648565:0.777771:0.648565:0.764056:0.633232:0.764056:0.000000 5 5:@0.796596:0.778326:0.834171:0.778326:0.834171:0.761892:0.796596:0.761892:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.807720:0.777771:0.823053:0.777771:0.823053:0.764056:0.807720:0.764056:0.000000 2. Propiedad multiplicativa de la igualdad.:@0.293660:0.803187:0.609741:0.803187:0.609741:0.786753:0.293660:0.786753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si, , entonces, :@0.323788:0.828052:0.549312:0.828049:0.549312:0.811615:0.323788:0.811618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.343079:0.828052:0.352337:0.828052:0.352337:0.811646:0.343079:0.811646:0.000000 5:@0.354493:0.827494:0.369826:0.827494:0.369826:0.813778:0.354493:0.813778:0.000000 b:@0.371955:0.828049:0.381213:0.828049:0.381213:0.811642:0.371955:0.811642:0.000000 a:@0.462463:0.828049:0.471722:0.828049:0.471722:0.811642:0.462463:0.811642:0.000000 3 5 3:@0.473892:0.827494:0.545373:0.827494:0.545373:0.813778:0.473892:0.813778:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.491354:0.828049:0.499011:0.828049:0.499011:0.811642:0.491354:0.811642:0.000000 b:@0.518627:0.828049:0.527886:0.828049:0.527886:0.811642:0.518627:0.811642:0.000000 c, y, :@0.547501:0.828049:0.574722:0.828049:0.574722:0.811642:0.547501:0.811642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a (c 0):@0.574677:0.828049:0.716654:0.828049:0.716654:0.811615:0.574677:0.811615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 5 4:@0.585174:0.827494:0.656655:0.827494:0.656655:0.813778:0.585174:0.813778:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.602636:0.828049:0.610293:0.828049:0.610293:0.811642:0.602636:0.811642:0.000000 b:@0.629909:0.828049:0.639168:0.828049:0.639168:0.811642:0.629909:0.811642:0.000000 c:@0.658783:0.828049:0.666440:0.828049:0.666440:0.811642:0.658783:0.811642:0.000000 Þ:@0.685397:0.827494:0.700730:0.827494:0.700730:0.813778:0.685397:0.813778:0.000000 Ejemplo::@0.323781:0.852910:0.390102:0.852910:0.390102:0.836241:0.323781:0.836241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8 7 1 entonces 8 5 (7 1) 5 :@0.389994:0.852910:0.672543:0.852910:0.672543:0.836477:0.389994:0.836477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 1:@0.405429:0.852356:0.449347:0.852356:0.449347:0.838640:0.405429:0.838640:0.000000:0.000000:0.000000 3 5 1 3:@0.546788:0.852356:0.657468:0.852356:0.657468:0.838640:0.546788:0.838640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8 2 (7 1) 2:@0.701259:0.852910:0.834171:0.852910:0.834171:0.836477:0.701259:0.836477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 5 1 4:@0.712373:0.852356:0.823053:0.852356:0.823053:0.838640:0.712373:0.838640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 40 8 5 :@0.593521:0.877772:0.672543:0.877772:0.672543:0.861338:0.593521:0.861338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 3:@0.613551:0.877218:0.657468:0.877218:0.657468:0.863502:0.613551:0.863502:0.000000:0.000000:0.000000 4 8 2:@0.768022:0.877772:0.834171:0.877772:0.834171:0.861338:0.768022:0.861338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 4:@0.779136:0.877218:0.823053:0.877218:0.823053:0.863502:0.779136:0.863502:0.000000:0.000000:0.000000 40 40 :@0.613217:0.902633:0.672552:0.902633:0.672552:0.886199:0.613217:0.886199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.633234:0.902078:0.648567:0.902078:0.648567:0.888363:0.633234:0.888363:0.000000 4 4:@0.796598:0.902633:0.834171:0.902633:0.834171:0.886199:0.796598:0.886199:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.807720:0.902078:0.823053:0.902078:0.823053:0.888363:0.807720:0.888363:0.000000 Tema 8. Ecuaciones e inecuaciones :@0.073089:0.096915:0.591102:0.096915:0.591102:0.065673:0.073089:0.065673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Qué valor representa un cangrejo?:@0.293660:0.167374:0.550211:0.167374:0.550211:0.150940:0.293660:0.150940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Una ecuación es :@0.078581:0.275083:0.190932:0.275083:0.190932:0.260143:0.078581:0.260143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la igualdad de dos :@0.078581:0.290212:0.203148:0.290212:0.203148:0.275272:0.078581:0.275272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 expresiones matemáticas :@0.078581:0.305341:0.249554:0.305341:0.249554:0.290401:0.078581:0.290401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en las que puede haber :@0.078581:0.320470:0.238356:0.320470:0.238356:0.305530:0.078581:0.305530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una o más incógnitas. :@0.078581:0.335599:0.225792:0.335599:0.225792:0.320659:0.078581:0.320659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Usualmente la :@0.078581:0.350728:0.176969:0.350728:0.176969:0.335788:0.078581:0.335788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 representamos con las :@0.078581:0.365857:0.234256:0.365857:0.234256:0.350917:0.078581:0.350917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 letras x, y o z.:@0.078581:0.380986:0.163857:0.380986:0.163857:0.366046:0.078581:0.366046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.078581:0.233113:0.177272:0.233113:0.177272:0.217707:0.078581:0.217707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.248242:0.167195:0.248242:0.167195:0.232836:0.078581:0.232836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 36:@0.221862:0.151269:0.234481:0.151269:0.234481:0.139725:0.221862:0.139725:0.000000:0.000000 38:@0.244791:0.176718:0.257410:0.176718:0.257410:0.165175:0.244791:0.165175:0.000000:0.000000 +:@0.107647:0.150828:0.114496:0.150828:0.114496:0.140420:0.107647:0.140420:0.000000 +:@0.107647:0.175115:0.114496:0.175115:0.114496:0.164707:0.107647:0.164707:0.000000 +:@0.140965:0.150827:0.147815:0.150827:0.147815:0.140419:0.140965:0.140419:0.000000 +:@0.140965:0.175115:0.147815:0.175115:0.147815:0.164707:0.140965:0.164707:0.000000 +:@0.172952:0.175115:0.179802:0.175115:0.179802:0.164707:0.172952:0.164707:0.000000 +:@0.201535:0.175115:0.208385:0.175115:0.208385:0.164707:0.201535:0.164707:0.000000 +:@0.174855:0.150828:0.181705:0.150828:0.181705:0.140420:0.174855:0.140420:0.000000 =:@0.208090:0.150828:0.214940:0.150828:0.214940:0.140420:0.208090:0.140420:0.000000 =:@0.232673:0.175376:0.239523:0.175376:0.239523:0.164968:0.232673:0.164968:0.000000 DBA 9 Opera sobre números desconocidos y encuentra las operaciones apropiadas al contexto para resolver problema.:@0.289361:0.971366:0.916494:0.971366:0.916494:0.959414:0.289361:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Así como en una :@0.082322:0.524769:0.196942:0.524769:0.196942:0.509829:0.082322:0.509829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuación donde cada :@0.082322:0.539898:0.228960:0.539898:0.228960:0.524958:0.082322:0.524958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 parte tiene igual :@0.082322:0.555027:0.194124:0.555027:0.194124:0.540087:0.082322:0.540087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 importancia, en un :@0.082322:0.570156:0.211032:0.570156:0.211032:0.555216:0.082322:0.555216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 entorno de paz, cada :@0.082322:0.585284:0.225150:0.585284:0.225150:0.570345:0.082322:0.570345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 individuo tiene el :@0.082322:0.600413:0.200730:0.600413:0.200730:0.585474:0.082322:0.585474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derecho de ser tratado :@0.082322:0.615542:0.235982:0.615542:0.235982:0.600603:0.082322:0.600603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con igualdad y respeto. :@0.082322:0.630671:0.239668:0.630671:0.239668:0.615731:0.082322:0.615731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ambos conceptos :@0.082322:0.645800:0.206949:0.645800:0.206949:0.630860:0.082322:0.630860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fomentan la idea de :@0.082322:0.660929:0.218010:0.660929:0.218010:0.645989:0.082322:0.645989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 equidad, donde todas las :@0.082322:0.676058:0.252021:0.676058:0.252021:0.661118:0.082322:0.661118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 partes involucradas son :@0.082322:0.691187:0.241584:0.691187:0.241584:0.676247:0.082322:0.676247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 consideradas de manera :@0.082322:0.706316:0.247820:0.706316:0.247820:0.691376:0.082322:0.691376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 justa y se busca alcanzar :@0.082322:0.721445:0.246104:0.721445:0.246104:0.706505:0.082322:0.706505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un equilibrio armonioso. :@0.082322:0.736574:0.247299:0.736574:0.247299:0.721634:0.082322:0.721634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Cátedra de paz:@0.082322:0.488774:0.189075:0.488774:0.189075:0.473368:0.082322:0.473368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reto matemático:@0.304294:0.140212:0.426770:0.140212:0.426770:0.124806:0.304294:0.124806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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