35:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
Ecuaciones e inecuaciones con valor absoluto:@0.108233:0.080221:0.471042:0.080221:0.471042:0.062538:0.108233:0.062538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuaciones con valor absoluto:@0.108233:0.109023:0.349783:0.109023:0.349783:0.091340:0.108233:0.091340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vamos a explicar la resolución de ecuaciones a través de ejercicios.:@0.108233:0.125726:0.578800:0.125726:0.578800:0.109228:0.108233:0.109228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.108233:0.160803:0.238888:0.160803:0.238888:0.144016:0.108233:0.144016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.108233:0.177995:0.124589:0.177995:0.124589:0.161280:0.108233:0.161280:0.000000:0.000000:0.000000
  Halla la solución en   de la ecuación || | – 1| = 1.:@0.124590:0.177778:0.483269:0.177778:0.483269:0.161280:0.124590:0.161280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.273819:0.176809:0.287728:0.176809:0.287728:0.163362:0.273819:0.163362:0.000000
x:@0.408153:0.177894:0.415628:0.177894:0.415628:0.161425:0.408153:0.161425:0.000000
Tenemos :@0.108234:0.195129:0.177048:0.195129:0.177048:0.178631:0.108234:0.178631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  || | – 1| = 1   | | –1 = ±1. :@0.108234:0.212479:0.316160:0.212479:0.316160:0.195982:0.108234:0.195982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.131872:0.212595:0.139347:0.212595:0.139347:0.196126:0.131872:0.196126:0.000000
x:@0.235246:0.212595:0.242720:0.212595:0.242720:0.196126:0.235246:0.196126:0.000000
•  Es decir que | | – 1 = –1 o | | –1 = 1. :@0.108230:0.229830:0.387460:0.229830:0.387460:0.213333:0.108230:0.213333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.216674:0.229946:0.224149:0.229946:0.224149:0.213477:0.216674:0.213477:0.000000
x:@0.317354:0.229946:0.324829:0.229946:0.324829:0.213477:0.317354:0.213477:0.000000
•  En el caso | | – 1 = –1, por la propiedad cancelativa se tiene | | = 0, :@0.108230:0.247181:0.600012:0.247181:0.600012:0.230683:0.108230:0.230683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.200452:0.247297:0.207927:0.247297:0.207927:0.230828:0.200452:0.230828:0.000000
x:@0.553236:0.247297:0.560711:0.247297:0.560711:0.230828:0.553236:0.230828:0.000000
 :@0.595756:0.247181:0.599898:0.247181:0.599898:0.230683:0.595756:0.230683:0.000000
   de donde   = 0.:@0.108230:0.264532:0.236215:0.264532:0.236215:0.248034:0.108230:0.248034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.193690:0.264647:0.201165:0.264647:0.201165:0.248179:0.193690:0.248179:0.000000
1:@0.201167:0.267877:0.205873:0.267877:0.205873:0.258276:0.201167:0.258276:0.000000
•  En el caso | | –1 = 1, se tiene | | = 2. Tenemos   = –2 o   = 2. :@0.108236:0.281882:0.564629:0.281882:0.564629:0.265385:0.108236:0.265385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.200939:0.281998:0.208414:0.281998:0.208414:0.265529:0.200939:0.265529:0.000000
x:@0.334466:0.281998:0.341941:0.281998:0.341941:0.265529:0.334466:0.265529:0.000000
x:@0.450250:0.281998:0.457725:0.281998:0.457725:0.265529:0.450250:0.265529:0.000000
2:@0.457717:0.284555:0.462239:0.284555:0.462239:0.275773:0.457717:0.275773:0.000000
x:@0.518147:0.281998:0.525622:0.281998:0.525622:0.265529:0.518147:0.265529:0.000000
3:@0.525621:0.284555:0.530143:0.284555:0.530143:0.275773:0.525621:0.275773:0.000000
Conclusión :@0.108235:0.299696:0.201496:0.299696:0.201496:0.282750:0.108235:0.282750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: se verifica que el conjunto solución de la ecuación  :@0.194715:0.299233:0.599903:0.299233:0.599903:0.282736:0.194715:0.282736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
|| | – 1| = 1 es {–2, 0, 2}.:@0.108235:0.316584:0.277519:0.316584:0.277519:0.300086:0.108235:0.300086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.118253:0.316700:0.125728:0.316700:0.125728:0.300231:0.118253:0.300231:0.000000
2.:@0.108235:0.349232:0.120507:0.349232:0.120507:0.332518:0.108235:0.332518:0.000000:0.000000
  Halla la solución en   de la ecuación   + | | = 3.:@0.120506:0.349016:0.472538:0.349016:0.472538:0.332518:0.120506:0.332518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.273819:0.348047:0.287728:0.348047:0.287728:0.334600:0.273819:0.334600:0.000000
x:@0.398135:0.349132:0.405610:0.349132:0.405610:0.332663:0.398135:0.332663:0.000000
x:@0.429711:0.349132:0.437186:0.349132:0.437186:0.332663:0.429711:0.332663:0.000000
Si :@0.108234:0.366367:0.124186:0.366367:0.124186:0.349869:0.108234:0.349869:0.000000:0.000000:0.000000
x < 0 :@0.124186:0.366830:0.165375:0.366830:0.165375:0.349884:0.124186:0.349884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entonces:@0.165375:0.366367:0.230087:0.366367:0.230087:0.349869:0.165375:0.349869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  | | = – . :@0.108234:0.383718:0.183311:0.383718:0.183311:0.367220:0.108234:0.367220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.126863:0.383833:0.134338:0.383833:0.134338:0.367364:0.126863:0.367364:0.000000
x:@0.168939:0.383833:0.176414:0.383833:0.176414:0.367364:0.168939:0.367364:0.000000
•  Luego   + | | = 3,   –   = 3, 0 = 3 que es un absurdo. :@0.108234:0.401068:0.493843:0.401068:0.493843:0.384571:0.108234:0.384571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.169399:0.401184:0.176874:0.401184:0.176874:0.384715:0.169399:0.384715:0.000000
x:@0.200975:0.401184:0.208450:0.401184:0.208450:0.384715:0.200975:0.384715:0.000000
x x:@0.247944:0.401184:0.281677:0.401184:0.281677:0.384715:0.247944:0.384715:0.000000:0.000000:0.000000
•  La ecuación   + | | = 3 no tiene solución en el conjunto ]–∞; 0[.:@0.108234:0.418419:0.574835:0.418419:0.574835:0.401921:0.108234:0.401921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.210685:0.418535:0.218159:0.418535:0.218159:0.402066:0.210685:0.402066:0.000000
x:@0.242260:0.418535:0.249735:0.418535:0.249735:0.402066:0.242260:0.402066:0.000000
Si :@0.108234:0.450851:0.124186:0.450851:0.124186:0.434353:0.108234:0.434353:0.000000:0.000000:0.000000
x ≥ 0 :@0.124186:0.451313:0.165375:0.451313:0.165375:0.434367:0.124186:0.434367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entonces:@0.165375:0.450851:0.230087:0.450851:0.230087:0.434353:0.165375:0.434353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| | =   y la ecuación se escribe como::@0.108234:0.468201:0.377077:0.468201:0.377077:0.451704:0.108234:0.451704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.113243:0.468317:0.120718:0.468317:0.120718:0.451848:0.113243:0.451848:0.000000
x, :@0.144819:0.468317:0.159402:0.468317:0.159402:0.451848:0.144819:0.451848:0.000000:0.000000:0.000000
x:@0.186547:0.491292:0.194022:0.491292:0.194022:0.474823:0.186547:0.474823:0.000000
 + | | = 3,   +   = 3   2  = 3, x =     [0, ∞[ ::@0.194022:0.491177:0.517446:0.491175:0.517446:0.474678:0.194022:0.474679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.218123:0.491292:0.225598:0.491292:0.225598:0.474823:0.218123:0.474823:0.000000
x x:@0.265092:0.491292:0.299133:0.491292:0.299133:0.474823:0.265092:0.474823:0.000000:0.000000:0.000000
⇒:@0.330863:0.490671:0.349878:0.490671:0.349878:0.472958:0.330863:0.472958:0.000000
x:@0.362516:0.491292:0.369991:0.491292:0.369991:0.474823:0.362516:0.474823:0.000000
3:@0.434432:0.482384:0.442928:0.482384:0.442928:0.465887:0.434432:0.465887:0.000000
2:@0.434432:0.498723:0.442928:0.498723:0.442928:0.482225:0.434432:0.482225:0.000000
:@0.449941:0.490958:0.465989:0.490958:0.465989:0.476312:0.449941:0.476312:0.000000
Conclusión :@0.108233:0.508989:0.201496:0.508989:0.201496:0.492043:0.108233:0.492043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: se verifica que la solución de la ecuación   + | | = 3 es :@0.194715:0.508526:0.599898:0.508526:0.599898:0.492028:0.194715:0.492028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.500971:0.508642:0.508446:0.508642:0.508446:0.492173:0.500971:0.492173:0.000000
x:@0.534396:0.508642:0.541871:0.508642:0.541871:0.492173:0.534396:0.492173:0.000000
x =  .:@0.108233:0.531501:0.152316:0.531497:0.152316:0.514999:0.108233:0.515004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.138195:0.522706:0.146691:0.522706:0.146691:0.506208:0.138195:0.506208:0.000000
2:@0.138195:0.539045:0.146691:0.539045:0.146691:0.522547:0.138195:0.522547:0.000000
Inecuaciones con valor absoluto:@0.108233:0.567441:0.365664:0.567441:0.365664:0.549759:0.108233:0.549759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Muchas inecuaciones con valor absoluto pueden resolverse en  , :@0.108233:0.584149:0.599897:0.584149:0.599897:0.567651:0.108233:0.567651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.579091:0.583180:0.593001:0.583180:0.593001:0.569733:0.579091:0.569733:0.000000
aplicando el siguiente teorema.:@0.108229:0.601500:0.328357:0.601500:0.328357:0.585002:0.108229:0.585002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema. :@0.108234:0.635652:0.183733:0.635652:0.183733:0.618706:0.108234:0.618706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean        . Entonces::@0.183733:0.635189:0.354133:0.635195:0.354133:0.618698:0.183733:0.618691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.221531:0.635305:0.230509:0.635305:0.230509:0.618836:0.221531:0.618836:0.000000
:@0.234651:0.634972:0.250699:0.634972:0.250699:0.620325:0.234651:0.620325:0.000000
R:@0.254842:0.634220:0.268751:0.634220:0.268751:0.620774:0.254842:0.620774:0.000000
+:@0.272891:0.628844:0.279192:0.628844:0.279192:0.619226:0.272891:0.619226:0.000000
i) :@0.108231:0.652763:0.122854:0.652763:0.122854:0.636048:0.108231:0.636048:0.000000:0.000000:0.000000
  | | <         ] – ,  [ .:@0.122855:0.652546:0.293456:0.652546:0.293456:0.636048:0.122855:0.636048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.136975:0.652662:0.144450:0.652662:0.144450:0.636193:0.136975:0.636193:0.000000
a:@0.168551:0.652662:0.177529:0.652662:0.177529:0.636193:0.168551:0.636193:0.000000
x:@0.203545:0.652662:0.211020:0.652662:0.211020:0.636193:0.203545:0.636193:0.000000
:@0.215162:0.652329:0.231210:0.652329:0.231210:0.637682:0.215162:0.637682:0.000000
a a:@0.255850:0.652662:0.280702:0.652662:0.280702:0.636193:0.255850:0.636193:0.000000:0.000000:0.000000
ii) :@0.108240:0.677242:0.127120:0.677242:0.127120:0.660527:0.108240:0.660527:0.000000:0.000000:0.000000:0.000000
 | | >         ] –∞, – [   ] , ∞[ .:@0.127120:0.677026:0.372270:0.677026:0.372270:0.660528:0.127120:0.660528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.136984:0.677141:0.144458:0.677141:0.144458:0.660673:0.136984:0.660673:0.000000
a:@0.168559:0.677141:0.177537:0.677141:0.177537:0.660673:0.168559:0.660673:0.000000
x:@0.203545:0.677141:0.211020:0.677141:0.211020:0.660673:0.203545:0.660673:0.000000
:@0.215162:0.676809:0.231210:0.676809:0.231210:0.662162:0.215162:0.662162:0.000000
a:@0.286559:0.677141:0.295537:0.677141:0.295537:0.660673:0.286559:0.660673:0.000000
∪:@0.305535:0.676520:0.320331:0.676520:0.320331:0.658807:0.305535:0.658807:0.000000
a:@0.330330:0.677141:0.339307:0.677141:0.339307:0.660673:0.330330:0.660673:0.000000
Ejercicios resueltos :@0.108240:0.711091:0.243210:0.711091:0.243210:0.694304:0.108240:0.694304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.108240:0.728283:0.124596:0.728283:0.124596:0.711568:0.108240:0.711568:0.000000:0.000000:0.000000
  Consideremos la inecuación | | < 5. Al aplicar el teorema prece-:@0.124595:0.728066:0.595760:0.728066:0.595760:0.711568:0.124595:0.711568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.344582:0.728182:0.352057:0.728182:0.352057:0.711713:0.344582:0.711713:0.000000
dente, tenemos::@0.131975:0.745417:0.245503:0.745417:0.245503:0.728919:0.131975:0.728919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| | < 5       ]–5, 5[   –5 <   < 5.:@0.131975:0.762767:0.382881:0.762774:0.382881:0.746276:0.131975:0.746270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.136984:0.762883:0.144458:0.762883:0.144458:0.746414:0.136984:0.746414:0.000000
x:@0.203063:0.762889:0.210537:0.762889:0.210537:0.746421:0.203063:0.746421:0.000000
:@0.214679:0.762557:0.230727:0.762557:0.230727:0.747910:0.214679:0.747910:0.000000
x:@0.345063:0.762889:0.352538:0.762889:0.352538:0.746421:0.345063:0.746421:0.000000
2. :@0.108236:0.792921:0.124592:0.792921:0.124592:0.776206:0.108236:0.776206:0.000000:0.000000:0.000000
  Halla el conjunto solución de la inecuación |3x – 8| < 2. Por el :@0.124592:0.792704:0.599903:0.792704:0.599903:0.776206:0.124592:0.776206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
teorema precedente, obtenemos::@0.131971:0.810055:0.367772:0.810055:0.367772:0.793557:0.131971:0.793557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
|3  – 8| < 2   –2 < 3 – 8 < 2  :@0.131985:0.827399:0.328699:0.827399:0.328699:0.810901:0.131985:0.810901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.143898:0.827515:0.151223:0.827515:0.151223:0.811046:0.143898:0.811046:0.000000
x:@0.269491:0.827515:0.276817:0.827515:0.276817:0.811046:0.269491:0.811046:0.000000
6 < 3  < 10  :@0.131970:0.844750:0.210215:0.844750:0.210215:0.828252:0.131970:0.828252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.164028:0.844865:0.171353:0.844865:0.171353:0.828397:0.164028:0.828397:0.000000
 2 <   < :@0.148683:0.866463:0.200528:0.866463:0.200528:0.849966:0.148683:0.849966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.176475:0.866579:0.183800:0.866579:0.183800:0.850110:0.176475:0.850110:0.000000
10:@0.202991:0.858920:0.219983:0.858920:0.219983:0.842422:0.202991:0.842422:0.000000:0.000000
3:@0.207230:0.875258:0.215726:0.875258:0.215726:0.858760:0.207230:0.858760:0.000000
       ]2,   :@0.222448:0.866463:0.313711:0.866463:0.313711:0.849966:0.222448:0.849966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.245952:0.866579:0.253278:0.866579:0.253278:0.850110:0.245952:0.850110:0.000000
:@0.256015:0.866246:0.271742:0.866246:0.271742:0.851600:0.256015:0.851600:0.000000
10:@0.292990:0.858920:0.309982:0.858920:0.309982:0.842422:0.292990:0.842422:0.000000:0.000000
3:@0.297229:0.875258:0.305725:0.875258:0.305725:0.858760:0.297229:0.858760:0.000000
[.:@0.313050:0.866463:0.320987:0.866463:0.320987:0.849966:0.313050:0.849966:0.000000:0.000000
3. :@0.108241:0.897868:0.124597:0.897868:0.124597:0.881154:0.108241:0.881154:0.000000:0.000000:0.000000
  Consideremos la ecuación | | > 2. Por el teorema precedente, :@0.124597:0.897651:0.599945:0.897651:0.599945:0.881153:0.124597:0.881153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.337342:0.897766:0.344817:0.897766:0.344817:0.881298:0.337342:0.881298:0.000000
 :@0.595768:0.897651:0.599910:0.897651:0.599910:0.881153:0.595768:0.881153:0.000000
tenemos::@0.131976:0.915001:0.197245:0.915001:0.197245:0.898504:0.131976:0.898504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| | > 2     < – 2  o    > 2 :@0.131976:0.932353:0.318076:0.932346:0.318076:0.915848:0.131976:0.915855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.136985:0.932468:0.144460:0.932468:0.144460:0.915999:0.136985:0.915999:0.000000
x:@0.203063:0.932461:0.210537:0.932461:0.210537:0.915993:0.203063:0.915993:0.000000
x:@0.278871:0.932461:0.286346:0.932461:0.286346:0.915993:0.278871:0.915993:0.000000
     ]–∞, –2[   ]2, ∞[ .:@0.131974:0.949696:0.299736:0.949696:0.299736:0.933199:0.131974:0.933199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.136116:0.949812:0.143591:0.949812:0.143591:0.933343:0.136116:0.933343:0.000000
:@0.147733:0.949480:0.163781:0.949480:0.163781:0.934833:0.147733:0.934833:0.000000
∪:@0.233482:0.949190:0.248278:0.949190:0.248278:0.931478:0.233482:0.931478:0.000000
Interdisciplinariedad:@0.684805:0.629282:0.831590:0.629282:0.831590:0.613810:0.684805:0.613810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y Música:@0.685042:0.658333:0.835083:0.658333:0.835083:0.642861:0.685042:0.642861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los intervalos y las inecuaciones :@0.638498:0.680882:0.849874:0.680882:0.849874:0.665819:0.638498:0.665819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en música miden la distancia :@0.638498:0.696724:0.829471:0.696724:0.829471:0.681661:0.638498:0.681661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre dos notas musicales. :@0.638498:0.712566:0.812460:0.712566:0.812460:0.697503:0.638498:0.697503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Conocer los intervalos permite :@0.638498:0.728408:0.841959:0.728408:0.841959:0.713345:0.638498:0.713345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
construir notas musicales.:@0.638498:0.744250:0.805934:0.744250:0.805934:0.729187:0.638498:0.729187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 24971728:@0.869050:0.921448:0.869050:0.856601:0.857581:0.856601:0.857581:0.921448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 384011941:@0.869303:0.525038:0.869303:0.456864:0.857834:0.456864:0.857834:0.525038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.685058:0.086801:0.831843:0.086801:0.831843:0.071329:0.685058:0.071329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.685294:0.115852:0.775373:0.115852:0.775373:0.100380:0.685294:0.100380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y Farmacología:@0.638751:0.131694:0.742620:0.131694:0.742620:0.116222:0.638751:0.116222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La contribución de la matemá-:@0.638751:0.154243:0.838748:0.154243:0.838748:0.139179:0.638751:0.139179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tica a la salud de las personas :@0.638751:0.170085:0.831446:0.170085:0.831446:0.155021:0.638751:0.155021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es infinita. Así, en la medicina, :@0.638751:0.185927:0.835425:0.185927:0.835425:0.170863:0.638751:0.170863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para que un medicamento sea :@0.638751:0.201769:0.840402:0.201769:0.840402:0.186705:0.638751:0.186705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
efectivo, se necesita un cierto :@0.638751:0.217611:0.832572:0.217611:0.832572:0.202547:0.638751:0.202547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nivel del fármaco en el torrente :@0.638751:0.233453:0.844342:0.233453:0.844342:0.218389:0.638751:0.218389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sanguíneo. El control de la can-:@0.638751:0.249294:0.840015:0.249294:0.840015:0.234231:0.638751:0.234231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tidad del fármaco en la sangre :@0.638751:0.265136:0.836637:0.265136:0.836637:0.250073:0.638751:0.250073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
le permite al médico asegurarse :@0.638751:0.280978:0.847524:0.280978:0.847524:0.265915:0.638751:0.265915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de que sus niveles estén dentro :@0.638751:0.296820:0.844340:0.296820:0.844340:0.281757:0.638751:0.281757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del intervalo adecuado. Por :@0.638751:0.312662:0.819221:0.312662:0.819221:0.297599:0.638751:0.297599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejemplo, la amikacina se aplica :@0.638751:0.328504:0.839890:0.328504:0.839890:0.313441:0.638751:0.313441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el intervalo [15, 25] mcg/mL.:@0.638751:0.344346:0.844062:0.344346:0.844062:0.329283:0.638751:0.329283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000