102:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8.º EGB:@0.120102:0.967458:0.170641:0.967458:0.170641:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DUA:@0.070720:0.123711:0.114363:0.123711:0.114363:0.103460:0.070720:0.103460:0.000000:0.000000:0.000000
. Representación:@0.114363:0.123082:0.246653:0.123082:0.246653:0.106182:0.114363:0.106182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En los temas anteriores revisamos la solución de ecuaciones e inecuaciones de primer :@0.287495:0.150303:0.907676:0.150303:0.907676:0.133914:0.287495:0.133914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
grado con números enteros. En este tema trataremos el estudio de las ecuaciones :@0.287495:0.166899:0.907748:0.166899:0.907748:0.150510:0.287495:0.150510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e inecuaciones que contienen en sus coeficientes y en su solución números fraccio-:@0.287495:0.183496:0.903714:0.183496:0.903714:0.167107:0.287495:0.167107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
narios o decimales.:@0.287495:0.200092:0.426917:0.200092:0.426917:0.183703:0.287495:0.183703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuaciones con números racionales :@0.287495:0.239977:0.649657:0.239977:0.649657:0.218467:0.287495:0.218467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Estas ecuaciones se presentan cuando en diversas situaciones se tienen expresiones :@0.287495:0.269886:0.907641:0.269886:0.907641:0.253497:0.287495:0.253497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fraccionarias, como la tercera parte de un número, la mitad de una edad, las tres :@0.287495:0.286482:0.907766:0.286482:0.907766:0.270093:0.287495:0.270093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuartas partes de una cantidad, etc.; por lo que los coeficientes y la solución pueden :@0.287495:0.303079:0.907685:0.303079:0.907685:0.286690:0.287495:0.286690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ser números racionales.:@0.287495:0.319675:0.459055:0.319675:0.459055:0.303286:0.287495:0.303286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las ecuaciones con números racionales tienen la misma estructura que las ecuacio-:@0.287495:0.343394:0.903585:0.343394:0.903585:0.327005:0.287495:0.327005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nes con números enteros.:@0.287495:0.359990:0.477040:0.359990:0.477040:0.343602:0.287495:0.343602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.554065:0.404960:0.565047:0.404960:0.565047:0.388336:0.554065:0.388336:0.000000
+:@0.618672:0.404960:0.629655:0.404960:0.629655:0.388336:0.618672:0.388336:0.000000
= :@0.589390:0.404960:0.606915:0.404960:0.606915:0.388336:0.589390:0.388336:0.000000:0.000000
5     :@0.609550:0.404960:0.638721:0.404960:0.638721:0.388571:0.609550:0.388571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.541184:0.396192:0.548647:0.396192:0.548647:0.379831:0.541184:0.379831:0.000000
2:@0.541184:0.415803:0.550176:0.415803:0.550176:0.399414:0.541184:0.399414:0.000000
3:@0.568936:0.396192:0.577928:0.396192:0.577928:0.379803:0.568936:0.379803:0.000000
4:@0.568936:0.415803:0.577928:0.415803:0.577928:0.399414:0.568936:0.399414:0.000000
1:@0.634404:0.395972:0.643397:0.395972:0.643397:0.379583:0.634404:0.379583:0.000000
2:@0.634570:0.415583:0.643563:0.415583:0.643563:0.399194:0.634570:0.399194:0.000000
Primer:@0.546328:0.431442:0.572372:0.431442:0.572372:0.422502:0.546328:0.422502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
miembro:@0.540750:0.440494:0.577940:0.440494:0.577940:0.431555:0.540750:0.431555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Segundo:@0.609049:0.431442:0.645646:0.431442:0.645646:0.422502:0.609049:0.422502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
miembro:@0.608748:0.440494:0.645938:0.440494:0.645938:0.431555:0.608748:0.431555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  ecuación con números racionales es un número que hace verdadera la igualdad :@0.287495:0.502210:0.892168:0.501024:0.892168:0.484635:0.287495:0.485821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.347804:0.502210:0.351839:0.502210:0.351839:0.485821:0.347804:0.485821:0.000000
 :@0.408114:0.502210:0.412149:0.502210:0.412149:0.485821:0.408114:0.485821:0.000000
             :@0.468422:0.502210:0.520885:0.502210:0.520885:0.485821:0.468422:0.485821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos::@0.287495:0.573976:0.357852:0.573976:0.357852:0.557338:0.287495:0.557338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  :@0.287495:0.607611:0.309351:0.607611:0.309351:0.590710:0.287495:0.590710:0.000000:0.000000:0.000000:0.000000
Resolvemos la siguiente ecuación:    +:@0.311230:0.607611:0.592010:0.608227:0.592010:0.591838:0.311230:0.591222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.569510:0.608227:0.576992:0.608227:0.576992:0.591866:0.569510:0.591866:0.000000
3:@0.598479:0.599265:0.607471:0.599265:0.607471:0.582876:0.598479:0.582876:0.000000
= −:@0.612539:0.608227:0.638540:0.608227:0.638540:0.591838:0.612539:0.591838:0.000000:0.000000:0.000000
3:@0.643829:0.599265:0.652822:0.599265:0.652822:0.582876:0.643829:0.582876:0.000000
4:@0.598479:0.619692:0.607471:0.619692:0.607471:0.603303:0.598479:0.603303:0.000000
5:@0.643829:0.619692:0.652822:0.619692:0.652822:0.603303:0.643829:0.603303:0.000000
Solución aplicando los axiomas de la igualdad.:@0.287494:0.649151:0.630828:0.649151:0.630828:0.632513:0.287494:0.632513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Restamos   a cada lado de la ecuación:   +:@0.287494:0.681445:0.605940:0.683410:0.605940:0.667021:0.287494:0.665056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.365444:0.674503:0.374437:0.674503:0.374437:0.658114:0.365444:0.658114:0.000000
4:@0.365444:0.694930:0.374437:0.694930:0.374437:0.678541:0.365444:0.678541:0.000000
y:@0.583440:0.683410:0.590922:0.683410:0.590922:0.667048:0.583440:0.667048:0.000000
3:@0.612408:0.674448:0.621401:0.674448:0.621401:0.658059:0.612408:0.658059:0.000000
−:@0.628035:0.683022:0.639018:0.683022:0.639018:0.666634:0.628035:0.666634:0.000000
3:@0.645891:0.674448:0.654884:0.674448:0.654884:0.658059:0.645891:0.658059:0.000000
= −:@0.661131:0.683410:0.687132:0.683036:0.687132:0.666647:0.661131:0.667021:0.000000:0.000000:0.000000
3:@0.693379:0.674462:0.702372:0.674462:0.702372:0.658073:0.693379:0.658073:0.000000
−:@0.708121:0.683036:0.719104:0.683036:0.719104:0.666647:0.708121:0.666647:0.000000
3:@0.724854:0.674462:0.733846:0.674462:0.733846:0.658073:0.724854:0.658073:0.000000
4:@0.612390:0.694889:0.621382:0.694889:0.621382:0.678500:0.612390:0.678500:0.000000
4:@0.645873:0.694889:0.654865:0.694889:0.654865:0.678500:0.645873:0.678500:0.000000
5:@0.693361:0.694889:0.702353:0.694889:0.702353:0.678500:0.693361:0.678500:0.000000
4:@0.724854:0.694889:0.733846:0.694889:0.733846:0.678500:0.724854:0.678500:0.000000
Reducimos términos:   + 0 = −:@0.287474:0.715883:0.512415:0.716481:0.512415:0.700092:0.287474:0.699494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.446352:0.716481:0.453833:0.716481:0.453833:0.700119:0.446352:0.700119:0.000000
27:@0.516598:0.707518:0.534583:0.707518:0.534583:0.691130:0.516598:0.691130:0.000000:0.000000
20:@0.516598:0.727946:0.534583:0.727946:0.534583:0.711557:0.516598:0.711557:0.000000:0.000000
Aplicamos la propiedad modulativa:  = −:@0.287505:0.756519:0.595301:0.756074:0.595301:0.739685:0.287505:0.740130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.555994:0.756448:0.563476:0.756448:0.563476:0.740086:0.555994:0.740086:0.000000
27:@0.599336:0.747499:0.617322:0.747499:0.617322:0.731110:0.599336:0.731110:0.000000:0.000000
20:@0.599336:0.767927:0.617322:0.767927:0.617322:0.751538:0.599336:0.751538:0.000000:0.000000
Solución aplicando la transposición de términos::@0.287485:0.804577:0.642726:0.804577:0.642726:0.787939:0.287485:0.787939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.287509:0.838948:0.294990:0.838948:0.294990:0.822587:0.287509:0.822587:0.000000
 +:@0.294990:0.838948:0.310009:0.838948:0.310009:0.822559:0.294990:0.822559:0.000000:0.000000
3:@0.316477:0.829986:0.325470:0.829986:0.325470:0.813597:0.316477:0.813597:0.000000
= −:@0.331127:0.838948:0.357128:0.838574:0.357128:0.822186:0.331127:0.822559:0.000000:0.000000:0.000000
3:@0.363025:0.830000:0.372018:0.830000:0.372018:0.813611:0.363025:0.813611:0.000000
4:@0.316495:0.850427:0.325488:0.850427:0.325488:0.834038:0.316495:0.834038:0.000000
5:@0.363025:0.850427:0.372018:0.850427:0.372018:0.834038:0.363025:0.834038:0.000000
 Pasamos :@0.377731:0.836832:0.449875:0.836832:0.449875:0.820443:0.377731:0.820443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.452741:0.829866:0.461734:0.829866:0.461734:0.813478:0.452741:0.813478:0.000000
4:@0.452741:0.850294:0.461734:0.850294:0.461734:0.833905:0.452741:0.833905:0.000000
a restar al segundo miembro:   = −:@0.287500:0.870043:0.541989:0.870588:0.541989:0.854199:0.287500:0.853655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.505576:0.871086:0.513058:0.871086:0.513058:0.854725:0.505576:0.854725:0.000000
3:@0.546799:0.862138:0.555792:0.862138:0.555792:0.845749:0.546799:0.845749:0.000000
−:@0.561007:0.870588:0.571990:0.870588:0.571990:0.854199:0.561007:0.854199:0.000000
3:@0.577205:0.862138:0.586197:0.862138:0.586197:0.845749:0.577205:0.845749:0.000000
5:@0.546818:0.882565:0.555810:0.882565:0.555810:0.866176:0.546818:0.866176:0.000000
4:@0.577205:0.882565:0.586197:0.882565:0.586197:0.866176:0.577205:0.866176:0.000000
Reducimos términos:   = −:@0.287522:0.904458:0.490024:0.904561:0.490024:0.888173:0.287522:0.888069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.450386:0.904935:0.457867:0.904935:0.457867:0.888574:0.450386:0.888574:0.000000
27:@0.494391:0.895987:0.512376:0.895987:0.512376:0.879598:0.494391:0.879598:0.000000:0.000000
20:@0.494391:0.916414:0.512376:0.916414:0.512376:0.900025:0.494391:0.900025:0.000000:0.000000
Ecuaciones e inecuaciones :@0.286308:0.063945:0.752534:0.063945:0.752534:0.027071:0.286308:0.027071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con números racionales :@0.286308:0.094120:0.706498:0.094120:0.706498:0.057246:0.286308:0.057246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.706498:0.101030:0.737778:0.101030:0.737778:0.055828:0.706498:0.055828:0.000000
:@0.094760:0.108604:0.183816:0.108604:0.183816:0.011516:0.094760:0.011516:0.000000:0.000000
Al igual que las ecuaciones con coeficientes enteros, la solución para una :@0.300882:0.484428:0.892185:0.484428:0.892185:0.468039:0.300882:0.468039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y se resuelve de dos formas: 1) aplicando los axiomas de la igualdad y 2) :@0.300882:0.517621:0.892059:0.517621:0.892059:0.501232:0.300882:0.501232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por transposición de términos.:@0.300882:0.534217:0.524645:0.534217:0.524645:0.517828:0.300882:0.517828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.049426:0.187206:0.049426:0.182099:0.037344:0.182099:0.037344:0.187206:0.000000
Shutterstock:@0.049426:0.182099:0.049426:0.144380:0.037515:0.144380:0.037515:0.182099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.909920:0.901846:0.909920:0.896738:0.897838:0.896738:0.897838:0.901846:0.000000
Shutterstock:@0.909920:0.896738:0.909920:0.859020:0.898009:0.859020:0.898009:0.896738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  +  6  =  9     +  6:@0.087367:0.501456:0.215189:0.501456:0.215189:0.485067:0.087367:0.485067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.076742:0.521067:0.084205:0.521067:0.084205:0.504706:0.076742:0.504706:0.000000
   +  6  =    9     +  6:@0.084021:0.521067:0.215778:0.521067:0.215778:0.504678:0.084021:0.504678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.165600:0.521067:0.173063:0.521067:0.173063:0.504706:0.165600:0.504706:0.000000
En años anteriores :@0.122499:0.372685:0.248425:0.372685:0.248425:0.357786:0.122499:0.357786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
realizabas ecuaciones :@0.100755:0.387773:0.248427:0.387773:0.248427:0.372874:0.100755:0.372874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando los ejercicios :@0.106032:0.402861:0.248425:0.402861:0.248425:0.387962:0.106032:0.387962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tenían un cajón para :@0.107657:0.417948:0.248427:0.417948:0.248427:0.403049:0.107657:0.403049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
completar las igualdades. :@0.075660:0.433036:0.248424:0.433036:0.248424:0.418137:0.075660:0.418137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ese cajón es ahora :@0.122600:0.448123:0.248427:0.448123:0.248427:0.433224:0.122600:0.433224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reemplazado en las :@0.115396:0.463211:0.248427:0.463211:0.248427:0.448312:0.115396:0.448312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones por letras.:@0.100604:0.478299:0.244757:0.478299:0.244757:0.463400:0.100604:0.463400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
     Matemática:@0.115799:0.340245:0.223340:0.340245:0.223340:0.323344:0.115799:0.323344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.082251:0.865339:0.082251:0.860232:0.070170:0.860232:0.070170:0.865339:0.000000
Shutterstock:@0.082251:0.860232:0.082251:0.822513:0.070340:0.822513:0.070340:0.860232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e historia:@0.088760:0.612648:0.244757:0.612648:0.244757:0.597283:0.088760:0.597283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los quipus fueron el :@0.109768:0.631293:0.248426:0.631293:0.248426:0.616394:0.109768:0.616394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
principal sistema de :@0.111493:0.646381:0.248426:0.646381:0.248426:0.631482:0.111493:0.631482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
registro de información :@0.088945:0.661469:0.248426:0.661469:0.248426:0.646570:0.088945:0.646570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los incas. Mediante :@0.097572:0.676556:0.248426:0.676556:0.248426:0.661657:0.097572:0.661657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.244757:0.676556:0.248426:0.676556:0.248426:0.661657:0.244757:0.661657:0.000000
cordeles anudados de :@0.097404:0.691644:0.248427:0.691644:0.248427:0.676745:0.097404:0.676745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distintos colores, se :@0.115581:0.706731:0.248426:0.706731:0.248426:0.691832:0.115581:0.691832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
registraba información :@0.094121:0.721819:0.248426:0.721819:0.248426:0.706920:0.094121:0.706920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
contable que se basó en :@0.081423:0.736907:0.248427:0.736907:0.248427:0.722008:0.081423:0.722008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un ordenamiento :@0.127408:0.751994:0.248426:0.751994:0.248426:0.737095:0.127408:0.737095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
decimal. Esto permitía :@0.097622:0.767082:0.248426:0.767082:0.248426:0.752183:0.097622:0.752183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representar cantidades :@0.092060:0.782169:0.248427:0.782169:0.248427:0.767270:0.092060:0.767270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desde las unidades hasta :@0.078424:0.797257:0.248427:0.797257:0.248427:0.782358:0.078424:0.782358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las decenas de millares.:@0.089648:0.812345:0.244755:0.812345:0.244755:0.797446:0.089648:0.797446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.090129:0.583490:0.247335:0.583490:0.247335:0.566589:0.090129:0.566589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.20. :@0.290067:0.965521:0.338404:0.965521:0.338404:0.954766:0.290067:0.954766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resolver ecuaciones e inecuaciones de primer grado con una incógnita en Q en la solución de problemas sencillos.:@0.338404:0.965521:0.874555:0.965521:0.874555:0.955091:0.338404:0.955091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000