44:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 Números naturales:@0.073089:0.043661:0.242487:0.043661:0.242487:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8.4 Inecuaciones:@0.293660:0.136836:0.424589:0.136836:0.424589:0.119889:0.293660:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Una inecuación es una desigualdad entre dos expresiones matemáticas que pueden :@0.293660:0.158845:0.931168:0.158845:0.931168:0.142411:0.293660:0.142411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 contener una o más variables.:@0.293660:0.175487:0.509684:0.175487:0.509684:0.159053:0.293660:0.159053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las expresiones matemáticas están conectadas por los signos::@0.293660:0.197496:0.743062:0.197496:0.743062:0.181062:0.293660:0.181062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.534628:0.218931:0.549961:0.218931:0.549961:0.205215:0.534628:0.205215:0.000000 , que se lee \mayor que\:@0.549869:0.219486:0.724024:0.219486:0.724024:0.203052:0.549869:0.203052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.534628:0.240933:0.549961:0.240933:0.549961:0.227218:0.534628:0.227218:0.000000 , que se lee \menor que\:@0.549869:0.241488:0.726615:0.241488:0.726615:0.225054:0.549869:0.225054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.534628:0.262936:0.549961:0.262936:0.549961:0.249220:0.534628:0.249220:0.000000 , que se lee \menor o igual que\:@0.549869:0.263491:0.779776:0.263491:0.779776:0.247057:0.549869:0.247057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 $:@0.534628:0.284938:0.549961:0.284938:0.549961:0.271223:0.534628:0.271223:0.000000 , que se lee \mayor o igual que\:@0.549869:0.285493:0.777184:0.285493:0.777184:0.269059:0.549869:0.269059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplo 4.:@0.293658:0.307502:0.373178:0.307502:0.373178:0.290832:0.293658:0.290832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La lista de desigualdades mostradas a continuación son inecuaciones.:@0.373067:0.307502:0.882343:0.307502:0.882343:0.291068:0.373067:0.291068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. 8x 2:@0.293660:0.329498:0.369250:0.329498:0.369250:0.313064:0.293660:0.313064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.342799:0.328944:0.358132:0.328944:0.358132:0.315228:0.342799:0.315228:0.000000 b. 3x 1 19:@0.293660:0.350428:0.406744:0.350428:0.406744:0.333994:0.293660:0.333994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 .:@0.342799:0.349873:0.386717:0.349873:0.386717:0.336157:0.342799:0.336157:0.000000:0.000000:0.000000 c. 10x 8 9x 12:@0.293660:0.371359:0.449819:0.371359:0.449819:0.354925:0.293660:0.354925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 #:@0.351702:0.370804:0.395620:0.370804:0.395620:0.357088:0.351702:0.357088:0.000000:0.000000:0.000000 1:@0.416686:0.370804:0.432019:0.370804:0.432019:0.357088:0.416686:0.357088:0.000000 d. 4x 26 90:@0.293660:0.392288:0.415647:0.392288:0.415647:0.375855:0.293660:0.375855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.342799:0.391734:0.358132:0.391734:0.358132:0.378018:0.342799:0.378018:0.000000 $:@0.380286:0.391734:0.395620:0.391734:0.395620:0.378018:0.380286:0.378018:0.000000 8.5 Propiedades de las desigualdades:@0.293660:0.414291:0.587676:0.414291:0.587676:0.397344:0.293660:0.397344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Propiedad aditiva de la desigualdad.:@0.293660:0.436293:0.585296:0.436293:0.585296:0.419860:0.293660:0.419860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si, , entonces, :@0.323788:0.458302:0.549312:0.458296:0.549312:0.441862:0.323788:0.441868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.343079:0.458302:0.352337:0.458302:0.352337:0.441896:0.343079:0.441896:0.000000 ,:@0.354493:0.457741:0.369826:0.457741:0.369826:0.444026:0.354493:0.444026:0.000000 b:@0.371955:0.458296:0.381213:0.458296:0.381213:0.441890:0.371955:0.441890:0.000000 a:@0.462463:0.458296:0.471722:0.458296:0.471722:0.441890:0.462463:0.441890:0.000000 1 , 1:@0.473892:0.457741:0.545373:0.457741:0.545373:0.444026:0.473892:0.444026:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.491352:0.458296:0.499010:0.458296:0.499010:0.441890:0.491352:0.441890:0.000000 b:@0.518625:0.458296:0.527884:0.458296:0.527884:0.441890:0.518625:0.441890:0.000000 c, y, a:@0.547500:0.458296:0.583905:0.458296:0.583905:0.441890:0.547500:0.441890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.583869:0.458296:0.661509:0.458296:0.661509:0.441862:0.583869:0.441862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 , 2:@0.586089:0.457741:0.657570:0.457741:0.657570:0.444026:0.586089:0.444026:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.603551:0.458296:0.611209:0.458296:0.611209:0.441890:0.603551:0.441890:0.000000 b:@0.630824:0.458296:0.640083:0.458296:0.640083:0.441890:0.630824:0.441890:0.000000 c:@0.659698:0.458296:0.667356:0.458296:0.667356:0.441890:0.659698:0.441890:0.000000 Ejemplo: 18 30, entonces, 18 6 30 6 :@0.323781:0.480298:0.654136:0.480298:0.654136:0.463865:0.323781:0.463865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.421037:0.479744:0.436370:0.479744:0.436370:0.466028:0.421037:0.466028:0.000000 1 ,:@0.557657:0.479744:0.601575:0.479744:0.601575:0.466028:0.557657:0.466028:0.000000:0.000000:0.000000 1:@0.623727:0.479744:0.639061:0.479744:0.639061:0.466028:0.623727:0.466028:0.000000 18 3 30 3:@0.673096:0.480298:0.785643:0.480298:0.785643:0.463865:0.673096:0.463865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 ,:@0.693121:0.479744:0.737039:0.479744:0.737039:0.466028:0.693121:0.466028:0.000000:0.000000:0.000000 2:@0.759191:0.479744:0.774525:0.479744:0.774525:0.466028:0.759191:0.466028:0.000000 24 36 :@0.594809:0.502301:0.654143:0.502301:0.654143:0.485867:0.594809:0.485867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.614825:0.501746:0.630158:0.501746:0.630158:0.488031:0.614825:0.488031:0.000000 15 27:@0.730257:0.502301:0.785649:0.502301:0.785649:0.485867:0.730257:0.485867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.750289:0.501746:0.765622:0.501746:0.765622:0.488031:0.750289:0.488031:0.000000 2. Propiedad multiplicativa de la desigualdad.:@0.293660:0.524304:0.635329:0.524304:0.635329:0.507870:0.293660:0.507870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si, , entonces, , (:@0.323788:0.546312:0.565326:0.546306:0.565326:0.529872:0.323788:0.529879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.343079:0.546312:0.352337:0.546312:0.352337:0.529906:0.343079:0.529906:0.000000 ,:@0.354493:0.545751:0.369826:0.545751:0.369826:0.532036:0.354493:0.532036:0.000000 b:@0.371955:0.546306:0.381213:0.546306:0.381213:0.529900:0.371955:0.529900:0.000000 a:@0.462463:0.546306:0.471722:0.546306:0.471722:0.529900:0.462463:0.529900:0.000000 3 , 3:@0.473892:0.545751:0.545373:0.545751:0.545373:0.532036:0.473892:0.532036:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.491354:0.546306:0.499011:0.546306:0.499011:0.529900:0.491354:0.529900:0.000000 b:@0.518627:0.546306:0.527886:0.546306:0.527886:0.529900:0.518627:0.529900:0.000000 c c:@0.547501:0.546306:0.572888:0.546306:0.572888:0.529900:0.547501:0.529900:0.000000:0.000000:0.000000 Þ:@0.572814:0.545751:0.588148:0.545751:0.588148:0.532036:0.572814:0.532036:0.000000 0) y, (c 0) y (:@0.588056:0.546306:0.782087:0.546306:0.782087:0.529872:0.588056:0.529872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.620176:0.546306:0.629435:0.546306:0.629435:0.529900:0.620176:0.529900:0.000000 4 , 4:@0.631592:0.545751:0.703073:0.545751:0.703073:0.532036:0.631592:0.532036:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.649054:0.546306:0.656711:0.546306:0.656711:0.529900:0.649054:0.529900:0.000000 b:@0.676327:0.546306:0.685586:0.546306:0.685586:0.529900:0.676327:0.529900:0.000000 c:@0.705201:0.546306:0.712859:0.546306:0.712859:0.529900:0.705201:0.529900:0.000000 Þ:@0.730086:0.545751:0.745419:0.545751:0.745419:0.532036:0.730086:0.532036:0.000000 c:@0.781963:0.546306:0.789620:0.546306:0.789620:0.529900:0.781963:0.529900:0.000000 .:@0.789547:0.545751:0.804880:0.545751:0.804880:0.532036:0.789547:0.532036:0.000000 0) :@0.804796:0.546306:0.822541:0.546306:0.822541:0.529872:0.804796:0.529872:0.000000:0.000000:0.000000 Ejemplo: 20 35, entonces, 20 5 35 5 20 5 35 5 :@0.323781:0.568309:0.787373:0.568309:0.787373:0.551875:0.323781:0.551875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.419306:0.567754:0.434640:0.567754:0.434640:0.554038:0.419306:0.554038:0.000000 3 ,:@0.557659:0.567754:0.601575:0.567754:0.601575:0.554038:0.557659:0.554038:0.000000:0.000000:0.000000 3:@0.623727:0.567754:0.639061:0.567754:0.639061:0.554038:0.623727:0.554038:0.000000 4 ,:@0.690912:0.567754:0.734830:0.567754:0.734830:0.554038:0.690912:0.554038:0.000000:0.000000:0.000000 :@0.706153:0.568309:0.710184:0.568309:0.710184:0.551875:0.706153:0.551875:0.000000 4 :@0.756982:0.567754:0.776825:0.567754:0.776825:0.554038:0.756982:0.554038:0.000000:0.000000 100 175 :@0.576991:0.590311:0.654151:0.590311:0.654151:0.573877:0.576991:0.573877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.605924:0.589756:0.621257:0.589756:0.621257:0.576041:0.605924:0.576041:0.000000 4 7:@0.748065:0.590311:0.785643:0.590311:0.785643:0.573877:0.748065:0.573877:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.759191:0.589756:0.774525:0.589756:0.774525:0.576041:0.759191:0.576041:0.000000 Solución de una inecuación::@0.293660:0.612314:0.506628:0.612314:0.506628:0.595644:0.293660:0.595644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Llamamos solución de una inecuación de primer grado en una variable al conjunto de :@0.293660:0.639676:0.931359:0.639676:0.931359:0.623242:0.293660:0.623242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 valores que puede tomar la variable y que hacen que se satisfaga la desigualdad. A este :@0.293660:0.656317:0.931309:0.656317:0.931309:0.639884:0.293660:0.639884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conjunto de valores se le conoce como :@0.293660:0.672959:0.582584:0.672959:0.582584:0.656525:0.293660:0.656525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conjunto solución de la inecuación.:@0.582267:0.672959:0.849933:0.672959:0.849933:0.656290:0.582267:0.656290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para lograr llegar a la solución, transformamos la inecuación inicial mediante la aplicación :@0.293660:0.700321:0.931300:0.700321:0.931300:0.683887:0.293660:0.683887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de las propiedades de las desigualdades, en otras inecuaciones equivalentes hasta lograr :@0.293660:0.716963:0.930415:0.716963:0.930415:0.700529:0.293660:0.700529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dejar la variable o incógnita a un solo lado de la desigualdad.:@0.293660:0.733605:0.733608:0.733605:0.733608:0.717171:0.293660:0.717171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Veamos un caso particular en el que solucionamos una inecuación en el conjunto de los :@0.293660:0.760967:0.931000:0.760967:0.931000:0.744533:0.293660:0.744533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números naturales.:@0.293660:0.777609:0.432123:0.777609:0.432123:0.761175:0.293660:0.761175:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. 3x 10 25 :@0.293660:0.804976:0.419604:0.804976:0.419604:0.788542:0.293660:0.788542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.342799:0.804421:0.358132:0.804421:0.358132:0.790705:0.342799:0.790705:0.000000 ,:@0.380286:0.804421:0.395620:0.804421:0.395620:0.790705:0.380286:0.790705:0.000000 :@0.474408:0.804976:0.478439:0.804976:0.478439:0.788542:0.474408:0.788542:0.000000 Esta es la inecuación inicial:@0.534631:0.804976:0.728809:0.804976:0.728809:0.788542:0.534631:0.788542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Empezamos con la aplicación la propiedad aditiva de las desigualdades con el fin de que :@0.293660:0.832339:0.930592:0.832339:0.930592:0.815905:0.293660:0.815905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el termino 3x quede sólo al lado izquierdo de la inecuación, para lo cual restamos 10 a :@0.293660:0.848981:0.930890:0.848981:0.930890:0.832547:0.293660:0.832547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ambos lados en inecuación inicial.:@0.293660:0.865622:0.540899:0.865622:0.540899:0.849189:0.293660:0.849189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2. 3x 10 10 25 10 :@0.293660:0.892986:0.494575:0.892986:0.494575:0.876552:0.293660:0.876552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.342799:0.892431:0.358132:0.892431:0.358132:0.878715:0.342799:0.878715:0.000000 2:@0.380286:0.892431:0.395620:0.892431:0.395620:0.878715:0.380286:0.878715:0.000000 ,:@0.417772:0.892431:0.433105:0.892431:0.433105:0.878715:0.417772:0.878715:0.000000 2:@0.455257:0.892431:0.470591:0.892431:0.470591:0.878715:0.455257:0.878715:0.000000 que se convierte en::@0.534629:0.892986:0.680973:0.892986:0.680973:0.876552:0.534629:0.876552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3. 3x 15:@0.293660:0.920349:0.378161:0.920349:0.378161:0.903915:0.293660:0.903915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.342799:0.919794:0.358132:0.919794:0.358132:0.906078:0.342799:0.906078:0.000000 DBA 8 (Ev. 3) Trabaja sobre números desconocidos y con esos números para dar respuestas a los problemas.:@0.348771:0.971341:0.914440:0.971341:0.914440:0.959389:0.348771:0.959389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Cátedra de :@0.083335:0.412729:0.164536:0.412729:0.164536:0.397323:0.083335:0.397323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ética y valores :@0.083335:0.427858:0.188018:0.427858:0.188018:0.412451:0.083335:0.412451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Alguna vez te has sentido :@0.082830:0.449266:0.244117:0.449266:0.244117:0.435821:0.082830:0.435821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 frustrado o confundido :@0.082830:0.461874:0.223969:0.461874:0.223969:0.448428:0.082830:0.448428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mientras tratas de encontrar :@0.082830:0.474480:0.253902:0.474480:0.253902:0.461034:0.082830:0.461034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 respuestas?:@0.082830:0.487086:0.151500:0.487086:0.151500:0.473640:0.082830:0.473640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Al resolver una ecuación, :@0.082830:0.499693:0.233756:0.499693:0.233756:0.486247:0.082830:0.486247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 buscamos encontar un :@0.082830:0.512299:0.223209:0.512299:0.223209:0.498853:0.082830:0.498853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 valor que complete todas :@0.082830:0.524905:0.238347:0.524905:0.238347:0.511459:0.082830:0.511459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sus partes de manera :@0.082830:0.537511:0.212897:0.537511:0.212897:0.524065:0.082830:0.524065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 adecuada. Esto significa :@0.082830:0.550117:0.226781:0.550117:0.226781:0.536671:0.082830:0.536671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que tenemos que ser :@0.082830:0.562723:0.212434:0.562723:0.212434:0.549278:0.082830:0.549278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pacientes, constantes y :@0.082830:0.575330:0.223808:0.575330:0.223808:0.561884:0.082830:0.561884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pensar de manera creativa :@0.082830:0.587936:0.243067:0.587936:0.243067:0.574490:0.082830:0.574490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para encontrar esa solución. :@0.082830:0.600542:0.252531:0.600542:0.252531:0.587096:0.082830:0.587096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Estos mismos principios :@0.082830:0.613148:0.228310:0.613148:0.228310:0.599702:0.082830:0.599702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pueden ayudarnos a resolver :@0.082830:0.625754:0.257961:0.625754:0.257961:0.612309:0.082830:0.612309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 problemas en la vida diaria.:@0.082830:0.638361:0.244311:0.638361:0.244311:0.624915:0.082830:0.624915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Estos mismos principios :@0.082830:0.754608:0.228310:0.754608:0.228310:0.741162:0.082830:0.741162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pueden ayudarnos a resolver :@0.082830:0.767214:0.257961:0.767214:0.257961:0.753768:0.082830:0.753768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 problemas en la vida diaria.:@0.082830:0.779820:0.244311:0.779820:0.244311:0.766374:0.082830:0.766374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000