134:@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
9.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
Ecuaciones lineales :@0.286308:0.063945:0.629182:0.063945:0.629182:0.027071:0.286308:0.027071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o de primer grado:@0.286308:0.094120:0.599149:0.094120:0.599149:0.057246:0.286308:0.057246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.094760:0.108604:0.159692:0.108604:0.159692:0.011516:0.094760:0.011516:0.000000
Una ecuación es una igualdad matemática que contiene una o más incógnitas :@0.304744:0.153866:0.907117:0.153866:0.907117:0.137477:0.304744:0.137477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y establece que dos expresiones son iguales entre sí. Las ecuaciones se utilizan :@0.304744:0.170462:0.907119:0.170462:0.907119:0.154073:0.304744:0.154073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para describir relaciones y situaciones en las matemáticas y en la ciencia, :@0.304744:0.187059:0.907123:0.187059:0.907123:0.170670:0.304744:0.170670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y  son una  herramienta  fundamental  para  resolver  problemas  y encontrar :@0.304744:0.203655:0.907136:0.203655:0.907136:0.187266:0.304744:0.187266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valores desconocidos.:@0.304744:0.220251:0.465541:0.220251:0.465541:0.203863:0.304744:0.203863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En este tema estudiaremos las ecuaciones lineales o de primer grado, que son :@0.304744:0.240416:0.907119:0.240416:0.907119:0.224027:0.304744:0.224027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aquellas ecuaciones que tienen una sola incógnita. Veamos un ejemplo.:@0.304744:0.257012:0.830202:0.257012:0.830202:0.240624:0.304744:0.240624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   es la longitud de una cuerda de guitarra medida desde la cejilla superior hasta :@0.304744:0.277177:0.907215:0.277177:0.907215:0.260788:0.304744:0.260788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.321144:0.277177:0.328607:0.277177:0.328607:0.260816:0.321144:0.260816:0.000000
el puente, y una octava se encuentra a 32 :@0.304744:0.293773:0.619303:0.293773:0.619303:0.277384:0.304744:0.277384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.620151:0.293773:0.642449:0.293773:0.642449:0.277412:0.620151:0.277412:0.000000:0.000000
 desde la cejilla superior, ¿cuál es la :@0.642449:0.293773:0.907051:0.293773:0.907051:0.277384:0.642449:0.277384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
longitud de la cuerda?:@0.304744:0.310370:0.468490:0.310370:0.468490:0.293981:0.304744:0.293981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Lo primero que hacemos  es plantear  una ecuación, tomando en cuenta :@0.304744:0.330534:0.907178:0.330534:0.907178:0.314145:0.304744:0.314145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el concepto musical de octava.:@0.304744:0.347131:0.531474:0.347131:0.531474:0.330742:0.304744:0.330742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.568418:0.356812:0.575881:0.356812:0.575881:0.340451:0.568418:0.340451:0.000000
cm:@0.620144:0.365774:0.642055:0.365774:0.642055:0.349413:0.620144:0.349413:0.000000:0.000000
2:@0.567684:0.376260:0.576677:0.376260:0.576677:0.359871:0.567684:0.359871:0.000000
32:@0.595170:0.365770:0.612953:0.365770:0.612953:0.349381:0.595170:0.349381:0.000000:0.000000
=:@0.581773:0.366448:0.591890:0.366448:0.591890:0.350875:0.581773:0.350875:0.000000
La longitud de la cuerda dividida por 2 corresponde a los 32 :@0.304750:0.391965:0.747526:0.391965:0.747526:0.375576:0.304750:0.375576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.747526:0.391965:0.769823:0.391965:0.769823:0.375604:0.747526:0.375604:0.000000:0.000000
.:@0.769823:0.391965:0.773030:0.391965:0.773030:0.375576:0.769823:0.375576:0.000000
Para resolver la ecuación aplicamos las reglas de resolución de ecuaciones.:@0.304750:0.412129:0.822587:0.412129:0.822587:0.395741:0.304750:0.395741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una ecuación tiene dos miembros, el primero antes del signo igual y el segundo :@0.314241:0.435957:0.898229:0.435957:0.898229:0.419568:0.314241:0.419568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
después de este. Para resolverla usamos el principio de trasposición :@0.314241:0.452304:0.898157:0.452304:0.898157:0.435915:0.314241:0.435915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de términos.:@0.314241:0.468651:0.405824:0.468651:0.405824:0.452262:0.314241:0.452262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.314241:0.488816:0.332281:0.488816:0.332281:0.471915:0.314241:0.471915:0.000000:0.000000:0.000000
Un término que está sumando en el primer miembro de una ecuación pasa :@0.337975:0.488816:0.898117:0.488816:0.898117:0.472427:0.337975:0.472427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al segundo miembro a restar.:@0.337975:0.505412:0.551179:0.505412:0.551179:0.489023:0.337975:0.489023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2. :@0.314241:0.525577:0.332281:0.525577:0.332281:0.508676:0.314241:0.508676:0.000000:0.000000:0.000000
Un término que está restando en el primer miembro de una ecuación pasa :@0.337975:0.525577:0.898192:0.525577:0.898192:0.509188:0.337975:0.509188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al segundo miembro a sumar.:@0.337975:0.542173:0.556192:0.542173:0.556192:0.525784:0.337975:0.525784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3. :@0.314241:0.562338:0.332281:0.562338:0.332281:0.545437:0.314241:0.545437:0.000000:0.000000:0.000000
Un término que está multiplicando en el primer miembro de una ecuación :@0.337975:0.562338:0.898100:0.562338:0.898100:0.545949:0.337975:0.545949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pasa al segundo miembro a dividir.:@0.337975:0.578934:0.593821:0.578934:0.593821:0.562545:0.337975:0.562545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4. :@0.314241:0.599099:0.332281:0.599099:0.332281:0.582198:0.314241:0.582198:0.000000:0.000000:0.000000
Un término que está dividiendo en el primer miembro de una ecuación :@0.337975:0.599099:0.898249:0.599099:0.898249:0.582710:0.337975:0.582710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pasa al segundo miembro a multiplicar.:@0.337975:0.615695:0.626731:0.615695:0.626731:0.599306:0.337975:0.599306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En nuestra ecuación, que tiene la forma :@0.304732:0.647712:0.618573:0.647712:0.618573:0.631324:0.304732:0.631324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.627485:0.639993:0.634949:0.639993:0.634949:0.623631:0.627485:0.623631:0.000000
a:@0.626596:0.659441:0.635865:0.659441:0.635865:0.643079:0.626596:0.643079:0.000000
b:@0.654237:0.648951:0.663506:0.648951:0.663506:0.632590:0.654237:0.632590:0.000000
=:@0.640840:0.649629:0.650957:0.649629:0.650957:0.634056:0.640840:0.634056:0.000000
, pasamos el término que está :@0.667173:0.647692:0.907138:0.647692:0.907138:0.631303:0.667173:0.631303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dividiendo a multiplicar. Así::@0.304757:0.664413:0.509024:0.664413:0.509024:0.648024:0.304757:0.648024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.310292:0.680187:0.317755:0.680187:0.317755:0.663826:0.310292:0.663826:0.000000
x:@0.382118:0.689146:0.389581:0.689146:0.389581:0.672784:0.382118:0.672784:0.000000
x:@0.485460:0.689146:0.492923:0.689146:0.492923:0.672784:0.485460:0.672784:0.000000
2:@0.309550:0.699643:0.318543:0.699643:0.318543:0.683254:0.309550:0.683254:0.000000
32:@0.337044:0.689146:0.354827:0.689146:0.354827:0.672757:0.337044:0.672757:0.000000:0.000000
 :@0.376092:0.689146:0.380128:0.689146:0.380128:0.672757:0.376092:0.672757:0.000000
2  32 :@0.407401:0.689146:0.460177:0.689146:0.460177:0.672757:0.407401:0.672757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.479434:0.689146:0.483470:0.689146:0.483470:0.672757:0.479434:0.672757:0.000000
64:@0.511111:0.689146:0.528894:0.689146:0.528894:0.672757:0.511111:0.672757:0.000000:0.000000
=:@0.323647:0.689823:0.333764:0.689823:0.333764:0.674250:0.323647:0.674250:0.000000
= ×:@0.394004:0.689823:0.431970:0.689823:0.431970:0.674250:0.394004:0.674250:0.000000:0.000000:0.000000
=:@0.497351:0.689823:0.507468:0.689823:0.507468:0.674250:0.497351:0.674250:0.000000
Por lo tanto, la longitud de la cuerda es 64 :@0.304744:0.718905:0.615706:0.718905:0.615706:0.702516:0.304744:0.702516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.615706:0.718905:0.638004:0.718905:0.638004:0.702543:0.615706:0.702543:0.000000:0.000000
.:@0.638004:0.718905:0.641210:0.718905:0.641210:0.702516:0.638004:0.702516:0.000000
Ejemplos::@0.304744:0.742624:0.375100:0.742624:0.375100:0.725986:0.304744:0.725986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a)  :@0.304744:0.766343:0.327281:0.766343:0.327281:0.749442:0.304744:0.749442:0.000000:0.000000:0.000000:0.000000
Resuelve las ecuaciones::@0.328478:0.766343:0.506747:0.766343:0.506747:0.749954:0.328478:0.749954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.304744:0.790062:0.323466:0.790062:0.323466:0.773161:0.304744:0.773161:0.000000:0.000000:0.000000
x:@0.328478:0.790062:0.335942:0.790062:0.335942:0.773700:0.328478:0.773700:0.000000
+ 8 = –9    :@0.339977:0.790062:0.429388:0.790062:0.429388:0.773673:0.339977:0.773673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.485666:0.790062:0.501883:0.790062:0.501883:0.773161:0.485666:0.773161:0.000000:0.000000
  :@0.505697:0.790062:0.513142:0.790062:0.513142:0.772926:0.505697:0.772926:0.000000:0.000000
 4  = –20    :@0.513142:0.790062:0.610320:0.790062:0.610320:0.773673:0.513142:0.773673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.526170:0.790062:0.533633:0.790062:0.533633:0.773700:0.526170:0.773700:0.000000
c):@0.666589:0.790062:0.680409:0.790062:0.680409:0.773161:0.666589:0.773161:0.000000:0.000000
   3  – 6 = 21:@0.684224:0.790062:0.776104:0.790062:0.776104:0.773673:0.684224:0.773673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.705324:0.790062:0.712787:0.790062:0.712787:0.773700:0.705324:0.773700:0.000000
Solución:@0.304744:0.817349:0.368522:0.817349:0.368522:0.800711:0.304744:0.800711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.304744:0.841068:0.323466:0.841068:0.323466:0.824167:0.304744:0.824167:0.000000:0.000000:0.000000
Esta ecuación es de la forma   +   =  . Pasamos al segundo miembro, el 8, con :@0.328478:0.841068:0.907125:0.841068:0.907125:0.824679:0.328478:0.824679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.540470:0.841068:0.547933:0.841068:0.547933:0.824706:0.540470:0.824706:0.000000
a:@0.567245:0.841068:0.576514:0.841068:0.576514:0.824706:0.567245:0.824706:0.000000
b:@0.595827:0.841068:0.605096:0.841068:0.605096:0.824706:0.595827:0.824706:0.000000
operación contraria es decir con –8.:@0.328497:0.857664:0.589910:0.857664:0.589910:0.841275:0.328497:0.841275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.567540:0.881383:0.575003:0.881383:0.575003:0.865022:0.567540:0.865022:0.000000
 + 8 = –9:@0.575003:0.881383:0.640311:0.881383:0.640311:0.864994:0.575003:0.864994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.568425:0.901548:0.575888:0.901548:0.575888:0.885186:0.568425:0.885186:0.000000
 = –9 – 8:@0.575888:0.901548:0.639426:0.901548:0.639426:0.885159:0.575888:0.885159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.577067:0.921712:0.584531:0.921712:0.584531:0.905351:0.577067:0.905351:0.000000
 = –17:@0.584531:0.921712:0.630784:0.921712:0.630784:0.905323:0.584531:0.905323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cejilla:@0.120102:0.196196:0.150538:0.196196:0.150538:0.184296:0.120102:0.184296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y música:@0.095965:0.396907:0.244877:0.396907:0.244877:0.381543:0.095965:0.381543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la mitad de una :@0.120424:0.415553:0.248546:0.415553:0.248546:0.400654:0.120424:0.400654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuerda, el sonido :@0.131313:0.430641:0.248546:0.430641:0.248546:0.415742:0.131313:0.415742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producido en su inicio es :@0.077789:0.445728:0.248546:0.445728:0.248546:0.430829:0.077789:0.430829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el mismo, pero en :@0.125332:0.460816:0.248544:0.460816:0.248544:0.445917:0.125332:0.445917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diferente frecuencia. En :@0.088577:0.475904:0.248544:0.475904:0.248544:0.461004:0.088577:0.461004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
música, a este intervalo se :@0.071523:0.490991:0.248543:0.490991:0.248543:0.476092:0.071523:0.476092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lo denomina octava.:@0.108797:0.506079:0.244875:0.506079:0.244875:0.491180:0.108797:0.491180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.090248:0.367748:0.247454:0.367748:0.247454:0.350847:0.090248:0.350847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.106337:0.327204:0.106337:0.322097:0.094255:0.322097:0.094255:0.327204:0.000000
Shutterstock:@0.106337:0.322097:0.106337:0.284378:0.094426:0.284378:0.094426:0.322097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una ecuación es una :@0.105983:0.587644:0.248546:0.587644:0.248546:0.572745:0.105983:0.572745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
igualdad que contiene :@0.093670:0.602731:0.248546:0.602731:0.248546:0.587832:0.093670:0.587832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una incógnita :@0.152622:0.617819:0.248546:0.617819:0.248546:0.602920:0.152622:0.602920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representada por una :@0.101091:0.632906:0.248546:0.632906:0.248546:0.618007:0.101091:0.618007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variable, en este caso x.:@0.090169:0.647994:0.244875:0.647994:0.244875:0.633095:0.090169:0.633095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.107846:0.667729:0.115309:0.667729:0.115309:0.652336:0.107846:0.652336:0.000000
65 83:@0.132446:0.667729:0.217822:0.667729:0.217822:0.652059:0.132446:0.652059:0.000000:0.000000:0.000000:0.000000:0.000000
imer:@0.126326:0.680489:0.144246:0.680489:0.144246:0.671568:0.126326:0.671568:0.000000:0.000000:0.000000:0.000000
miembro:@0.117419:0.688504:0.154253:0.688504:0.154253:0.679583:0.117419:0.679583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Segundo:@0.182415:0.679046:0.218224:0.679046:0.218224:0.670125:0.182415:0.670125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
miembro:@0.182223:0.687053:0.219078:0.687053:0.219078:0.678132:0.182223:0.678132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pr:@0.118070:0.680489:0.126197:0.680489:0.126197:0.671568:0.118070:0.671568:0.000000:0.000000
+− =+:@0.119206:0.668406:0.206074:0.668406:0.206074:0.652833:0.119206:0.652833:0.000000:0.000000:0.000000:0.000000:0.000000
     Matemática:@0.115918:0.555201:0.223459:0.555201:0.223459:0.538301:0.115918:0.538301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En economía y finanzas, :@0.085696:0.774510:0.248544:0.774510:0.248544:0.759611:0.085696:0.759611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los números negativos :@0.094072:0.789598:0.248544:0.789598:0.248544:0.774699:0.094072:0.774699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresan pérdidas :@0.123221:0.804685:0.248544:0.804685:0.248544:0.789786:0.123221:0.789786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o saldos en contra. :@0.120172:0.819773:0.248546:0.819773:0.248546:0.804874:0.120172:0.804874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mantener el control de los :@0.069815:0.834860:0.248544:0.834860:0.248544:0.819961:0.069815:0.819961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
gastos ayuda a tener una :@0.078174:0.849948:0.248544:0.849948:0.248544:0.835049:0.078174:0.835049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
economía sana.:@0.140627:0.865036:0.244877:0.865036:0.244877:0.850137:0.140627:0.850137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué otras estrategias :@0.105799:0.883681:0.247891:0.883681:0.247891:0.868808:0.105799:0.868808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mantienen una :@0.146139:0.898769:0.247893:0.898769:0.247893:0.883895:0.146139:0.883895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
economía equilibrada?:@0.098981:0.913857:0.244875:0.913857:0.244875:0.898983:0.098981:0.898983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Educación :@0.142530:0.734872:0.224214:0.734872:0.224214:0.717972:0.142530:0.717972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
financiera:@0.145716:0.748703:0.220766:0.748703:0.220766:0.731802:0.145716:0.731802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.150609:0.748703:0.154233:0.748703:0.154233:0.731802:0.150609:0.731802:0.000000
M.4.1.38. :@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 de primer grado con una incógnita en R para resolver problemas sencillos.:@0.338404:0.965521:0.780859:0.965521:0.780859:0.955091:0.338404:0.955091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.66.:@0.271550:0.791216:0.271550:0.761063:0.257654:0.761063:0.257654:0.791216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000