180:@0.052592:0.966074:0.080768:0.966074:0.080768:0.949450:0.052592:0.949450:0.000000:0.000000:0.000000
Tema 1:@0.124729:0.083964:0.219414:0.083964:0.219414:0.055923:0.124729:0.055923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuaciones lineales o de primer grado:@0.305303:0.083049:0.796568:0.083049:0.796568:0.055393:0.305303:0.055393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recordemos que una ecuación es una igualdad entre dos expresiones algebraicas, :@0.304744:0.218880:0.907143:0.218880:0.907143:0.203210:0.304744:0.203210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en la que figura uno o varios valores desconocidos, llamados incógnitas, además :@0.304744:0.235476:0.907139:0.235476:0.907139:0.219806:0.304744:0.219806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de ciertos datos conocidos.:@0.304744:0.252073:0.505122:0.252073:0.505122:0.236403:0.304744:0.236403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En este tema estudiaremos las ecuaciones lineales o de primer grado.:@0.304744:0.272237:0.812213:0.272237:0.812213:0.256567:0.304744:0.256567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   es la longitud de una cuerda de guitarra medida desde la cejilla superior hasta :@0.304744:0.292402:0.907215:0.292402:0.907215:0.276732:0.304744:0.276732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.321144:0.292402:0.328607:0.292402:0.328607:0.276040:0.321144:0.276040:0.000000
el puente, y una octava se encuentra a 32 :@0.304744:0.308998:0.619303:0.308998:0.619303:0.293328:0.304744:0.293328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.620151:0.308998:0.642449:0.308998:0.642449:0.292637:0.620151:0.292637:0.000000:0.000000
 desde la cejilla superior, ¿cuál es la :@0.642449:0.308998:0.907051:0.308998:0.907051:0.293328:0.642449:0.293328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
longitud de la cuerda?:@0.304744:0.325594:0.468490:0.325594:0.468490:0.309925:0.304744:0.309925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Lo  primero  que  hacemos  es  plantear  una  ecuación,  tomando  en  cuenta  el :@0.304744:0.345759:0.907119:0.345759:0.907119:0.330089:0.304744:0.330089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
concepto musical de octava.:@0.304744:0.362355:0.514594:0.362355:0.514594:0.346686:0.304744:0.346686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.568418:0.375600:0.575881:0.375600:0.575881:0.359239:0.568418:0.359239:0.000000
cm:@0.620144:0.384562:0.642055:0.384562:0.642055:0.368201:0.620144:0.368201:0.000000:0.000000
2:@0.567686:0.395049:0.576679:0.395049:0.576679:0.379379:0.567686:0.379379:0.000000
32:@0.595170:0.384558:0.612953:0.384558:0.612953:0.368888:0.595170:0.368888:0.000000:0.000000
=:@0.581773:0.385236:0.591890:0.385236:0.591890:0.369663:0.581773:0.369663:0.000000
La longitud de la cuerda dividida por 2 corresponde a los 32 :@0.304750:0.414321:0.747526:0.414321:0.747526:0.398651:0.304750:0.398651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.747526:0.414321:0.769823:0.414321:0.769823:0.397960:0.747526:0.397960:0.000000:0.000000
.:@0.769823:0.414321:0.773030:0.414321:0.773030:0.398651:0.769823:0.398651:0.000000
Para resolver la ecuación aplicamos las reglas de resolución de ecuaciones.:@0.304750:0.438040:0.822587:0.438040:0.822587:0.422370:0.304750:0.422370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una  ecuación  tiene  dos  miembros,  el  primero  antes  del  signo  igual  y  el :@0.319266:0.466694:0.891209:0.466694:0.891209:0.451024:0.319266:0.451024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
segundo después de este. Para resolverla usamos el principio de transposición :@0.315913:0.483041:0.894557:0.483041:0.894557:0.467371:0.315913:0.467371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de términos.:@0.315913:0.499389:0.407496:0.499389:0.407496:0.483719:0.315913:0.483719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Un término que está sumando en el primer miembro de una ecuación pasa :@0.315913:0.519304:0.894614:0.519304:0.894614:0.503635:0.315913:0.503635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al segundo miembro a restar.:@0.334911:0.535652:0.548115:0.535652:0.548115:0.519982:0.334911:0.519982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.  Un término que está restando en el primer miembro de una ecuación pasa :@0.315913:0.555567:0.894561:0.555567:0.894561:0.539898:0.315913:0.539898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al segundo miembro a sumar.:@0.334911:0.571915:0.553128:0.571915:0.553128:0.556245:0.334911:0.556245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.  Un término que está multiplicando en el primer miembro de una ecuación :@0.315913:0.591830:0.894629:0.591830:0.894629:0.576161:0.315913:0.576161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pasa al segundo miembro a dividir.:@0.334911:0.608178:0.590757:0.608178:0.590757:0.592508:0.334911:0.592508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.  Un término que está dividiendo en el primer miembro de una ecuación pasa :@0.315913:0.628094:0.894520:0.628094:0.894520:0.612424:0.315913:0.612424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
al segundo miembro a multiplicar.:@0.336588:0.644441:0.587532:0.644441:0.587532:0.628771:0.336588:0.628771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En nuestra ecuación, que tiene la forma :@0.304744:0.676634:0.618583:0.676634:0.618583:0.660964:0.304744:0.660964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.627485:0.668933:0.634949:0.668933:0.634949:0.652572:0.627485:0.652572:0.000000
a:@0.626596:0.688382:0.635865:0.688382:0.635865:0.672021:0.626596:0.672021:0.000000
b:@0.654237:0.677891:0.663506:0.677891:0.663506:0.661530:0.654237:0.661530:0.000000
=:@0.640840:0.678569:0.650957:0.678569:0.650957:0.662996:0.640840:0.662996:0.000000
, pasamos el término que está :@0.667173:0.676633:0.907138:0.676633:0.907138:0.660963:0.667173:0.660963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dividiendo a multiplicar. Así::@0.304757:0.693354:0.509024:0.693354:0.509024:0.677684:0.304757:0.677684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.310292:0.709129:0.317755:0.709129:0.317755:0.692768:0.310292:0.692768:0.000000
x:@0.382118:0.718087:0.389581:0.718087:0.389581:0.701726:0.382118:0.701726:0.000000
x:@0.485460:0.718087:0.492923:0.718087:0.492923:0.701726:0.485460:0.701726:0.000000
2:@0.309550:0.728585:0.318543:0.728585:0.318543:0.712915:0.309550:0.712915:0.000000
32:@0.337044:0.718087:0.354827:0.718087:0.354827:0.702418:0.337044:0.702418:0.000000:0.000000
2:@0.407401:0.718087:0.416393:0.718087:0.416393:0.702418:0.407401:0.702418:0.000000
32:@0.437825:0.718087:0.455607:0.718087:0.455607:0.702418:0.437825:0.702418:0.000000:0.000000
64:@0.511111:0.718087:0.528899:0.718087:0.528899:0.702418:0.511111:0.702418:0.000000:0.000000
=:@0.323634:0.718765:0.333750:0.718765:0.333750:0.703192:0.323634:0.703192:0.000000
= ×:@0.393990:0.718765:0.431970:0.718765:0.431970:0.703192:0.393990:0.703192:0.000000:0.000000:0.000000
=:@0.497351:0.718765:0.507468:0.718765:0.507468:0.703192:0.497351:0.703192:0.000000
Por lo tanto, la longitud de la cuerda es 64 :@0.304744:0.747846:0.615706:0.747846:0.615706:0.732177:0.304744:0.732177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.615706:0.747846:0.638004:0.747846:0.638004:0.731485:0.615706:0.731485:0.000000:0.000000
.:@0.638004:0.747846:0.641210:0.747846:0.641210:0.732177:0.638004:0.732177:0.000000
Ejemplo 1:@0.304744:0.766184:0.374249:0.766184:0.374249:0.751071:0.304744:0.751071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resolver las ecuaciones:@0.304744:0.790222:0.476323:0.790222:0.476323:0.774553:0.304744:0.774553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.333233:0.813941:0.352471:0.813941:0.352471:0.796806:0.333233:0.796806:0.000000:0.000000:0.000000
x:@0.361722:0.813941:0.369185:0.813941:0.369185:0.797580:0.361722:0.797580:0.000000
 + 8 = –9  :@0.369185:0.813941:0.442564:0.813941:0.442564:0.798272:0.369185:0.798272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.485663:0.813941:0.489698:0.813941:0.489698:0.798272:0.485663:0.798272:0.000000
b)   :@0.545980:0.813941:0.573806:0.813941:0.573806:0.796806:0.545980:0.796806:0.000000:0.000000:0.000000:0.000000:0.000000
 4  = –20    :@0.573806:0.813941:0.670634:0.813941:0.670634:0.798272:0.573806:0.798272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.586834:0.813941:0.594297:0.813941:0.594297:0.797580:0.586834:0.797580:0.000000
c):@0.726902:0.813941:0.741000:0.813941:0.741000:0.796806:0.726902:0.796806:0.000000:0.000000
    3  – 6 = 21:@0.741000:0.813941:0.836915:0.813941:0.836915:0.798272:0.741000:0.798272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.766135:0.813941:0.773598:0.813941:0.773598:0.797580:0.766135:0.797580:0.000000
Solución:@0.304744:0.835847:0.365404:0.835847:0.365404:0.820735:0.304744:0.820735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.333236:0.859887:0.352475:0.859887:0.352475:0.842751:0.333236:0.842751:0.000000:0.000000:0.000000
Esta ecuación es de la forma   +   =  . Pasamos al segundo miembro, el 8, :@0.361725:0.859887:0.907110:0.859887:0.907110:0.844217:0.361725:0.844217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.573275:0.859887:0.580738:0.859887:0.580738:0.843526:0.573275:0.843526:0.000000
a:@0.599903:0.859887:0.609172:0.859887:0.609172:0.843526:0.599903:0.843526:0.000000
b:@0.628336:0.859887:0.637605:0.859887:0.637605:0.843526:0.628336:0.843526:0.000000
con operación contraria es decir con –8.:@0.361725:0.876483:0.655073:0.876483:0.655073:0.860814:0.361725:0.860814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.567525:0.896648:0.574988:0.896648:0.574988:0.880287:0.567525:0.880287:0.000000
 + 8 = –9:@0.574988:0.896648:0.640296:0.896648:0.640296:0.880978:0.574988:0.880978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.568410:0.916813:0.575873:0.916813:0.575873:0.900451:0.568410:0.900451:0.000000
 = –9 – 8:@0.575873:0.916813:0.639411:0.916813:0.639411:0.901143:0.575873:0.901143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.577052:0.936977:0.584515:0.936977:0.584515:0.920616:0.577052:0.920616:0.000000
 = –17:@0.584515:0.936977:0.630769:0.936977:0.630769:0.921307:0.584515:0.921307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una ecuación es :@0.105654:0.590383:0.219068:0.590383:0.219068:0.576138:0.105654:0.576138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una igualdad que :@0.105654:0.605471:0.226741:0.605471:0.226741:0.591226:0.105654:0.591226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
contiene una incógnita :@0.105654:0.620559:0.264515:0.620559:0.264515:0.606313:0.105654:0.606313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representada por una :@0.105654:0.635646:0.253109:0.635646:0.253109:0.621401:0.105654:0.621401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variable, en este caso x.:@0.105654:0.650734:0.260361:0.650734:0.260361:0.636489:0.105654:0.636489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.119511:0.674599:0.126974:0.674599:0.126974:0.659205:0.119511:0.659205:0.000000
65 83:@0.144112:0.674599:0.229487:0.674599:0.229487:0.658929:0.144112:0.658929:0.000000:0.000000:0.000000:0.000000:0.000000
imer:@0.137990:0.687357:0.155911:0.687357:0.155911:0.678436:0.137990:0.678436:0.000000:0.000000:0.000000:0.000000
miembro:@0.129083:0.695373:0.165918:0.695373:0.165918:0.686452:0.129083:0.686452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Segundo:@0.194080:0.685915:0.229889:0.685915:0.229889:0.676994:0.194080:0.676994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
miembro:@0.193888:0.693922:0.230743:0.693922:0.230743:0.685001:0.193888:0.685001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pr:@0.129735:0.687357:0.137862:0.687357:0.137862:0.678436:0.129735:0.678436:0.000000:0.000000
+− =+:@0.130871:0.675276:0.217738:0.675276:0.217738:0.659703:0.130871:0.659703:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que...:@0.135707:0.565357:0.257788:0.565357:0.257788:0.548456:0.135707:0.548456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es el valor de   en cada igualdad para que se cumplan?:@0.311739:0.164987:0.757983:0.164987:0.757983:0.149317:0.311739:0.149317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.454830:0.164987:0.462293:0.164987:0.462293:0.148626:0.454830:0.148626:0.000000
3 +   = 7                    6  = 12                          4 –   = 10                   2  = –10     :@0.348060:0.188706:0.881098:0.188706:0.881098:0.173036:0.348060:0.173036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.376107:0.188706:0.383570:0.188706:0.383570:0.172345:0.376107:0.172345:0.000000
x:@0.501323:0.188706:0.508786:0.188706:0.508786:0.172345:0.501323:0.172345:0.000000
x:@0.677031:0.188706:0.684494:0.188706:0.684494:0.172345:0.677031:0.172345:0.000000
x:@0.807203:0.188706:0.814667:0.188706:0.814667:0.172345:0.807203:0.172345:0.000000
Desequilibrio cognitivo:@0.344944:0.138666:0.522699:0.138666:0.522699:0.121766:0.344944:0.121766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 250576867.:@0.093748:0.321900:0.093748:0.246622:0.082360:0.246622:0.082360:0.321900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cejilla:@0.120102:0.181939:0.150538:0.181939:0.150538:0.170040:0.120102:0.170040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la mitad de una :@0.106529:0.410587:0.234652:0.410587:0.234652:0.396342:0.106529:0.396342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuerda, el sonido :@0.106529:0.425674:0.223763:0.425674:0.223763:0.411429:0.106529:0.411429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producido en su inicio :@0.106529:0.440762:0.259244:0.440762:0.259244:0.426517:0.106529:0.426517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es el mismo, pero en :@0.106529:0.455850:0.247784:0.455850:0.247784:0.441604:0.106529:0.441604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diferente frecuencia. En :@0.106529:0.470937:0.266496:0.470937:0.266496:0.456692:0.106529:0.456692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
música, a este intervalo :@0.106529:0.486025:0.265506:0.486025:0.265506:0.471780:0.106529:0.471780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se lo denomina octava.:@0.106529:0.501112:0.260650:0.501112:0.260650:0.486867:0.106529:0.486867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia  :@0.136865:0.374859:0.250102:0.374859:0.250102:0.357959:0.136865:0.357959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.136865:0.388690:0.262394:0.388690:0.262394:0.371789:0.136865:0.371789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En economía y finanzas, :@0.106529:0.795866:0.269595:0.795866:0.269595:0.781621:0.106529:0.781621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los números negativos :@0.106529:0.810954:0.261002:0.810954:0.261002:0.796709:0.106529:0.796709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresan pérdidas :@0.106529:0.826042:0.231852:0.826042:0.231852:0.811797:0.106529:0.811797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o saldos en contra. :@0.106529:0.841129:0.234903:0.841129:0.234903:0.826884:0.106529:0.826884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mantener el control de :@0.106529:0.856217:0.262878:0.856217:0.262878:0.841972:0.106529:0.841972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los gastos ayuda a tener :@0.106529:0.871305:0.270130:0.871305:0.270130:0.857059:0.106529:0.857059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una economía sana.:@0.106529:0.886392:0.239929:0.886392:0.239929:0.872147:0.106529:0.872147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Expresa:@0.106529:0.908609:0.160472:0.908609:0.160472:0.893496:0.106529:0.893496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 tu opinión en :@0.160472:0.908609:0.258356:0.908609:0.258356:0.894363:0.160472:0.894363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la clase.:@0.106529:0.923696:0.157103:0.923696:0.157103:0.909451:0.106529:0.909451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia  :@0.136865:0.758882:0.247891:0.758882:0.247891:0.741981:0.136865:0.741981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
socioemocional:@0.136865:0.772712:0.259482:0.772712:0.259482:0.755811:0.136865:0.755811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.38. :@0.106411:0.954024:0.154748:0.954024:0.154748:0.943269:0.106411:0.943269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resolver ecuaciones de primer grado con una incógnita en R para resolver problemas sencillos.:@0.154748:0.954024:0.597203:0.954024:0.597203:0.944053:0.154748:0.944053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.430301:0.186233:0.436024:0.186233:0.436024:0.176262:0.430301:0.176262:0.000000
2:@0.577190:0.186233:0.582912:0.186233:0.582912:0.176262:0.577190:0.176262:0.000000
–6:@0.740249:0.186233:0.751835:0.186233:0.751835:0.176262:0.740249:0.176262:0.000000:0.000000
–5:@0.871565:0.184852:0.883151:0.184852:0.883151:0.174880:0.871565:0.174880:0.000000:0.000000