{"id":1155,"date":"2022-05-26T20:23:55","date_gmt":"2022-05-26T20:23:55","guid":{"rendered":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/?p=1155"},"modified":"2022-05-26T20:23:55","modified_gmt":"2022-05-26T20:23:55","slug":"clase-digital-6-desigualdades","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/clase-digital-6-desigualdades\/","title":{"rendered":"Clase digital 6. Desigualdades"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-40 has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-1156\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/776680.jpg\" style=\"object-position:59% 43%\" data-object-fit=\"cover\" data-object-position=\"59% 43%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1280\" height=\"853\" class=\"wp-block-cover__image-background wp-image-1156\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/776680.jpg\" style=\"object-position:59% 43%\" data-object-fit=\"cover\" data-object-position=\"59% 43%\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/776680.jpg 1280w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/776680-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/776680-1024x682.jpg 1024w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/776680-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/776680-272x182.jpg 272w\" sizes=\"auto, (max-width: 1280px) 100vw, 1280px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Desigualdades<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola! Es momento de informarte que estamos en la recta final del m\u00f3dulo y te comento que en esta clase abordaremos el tema de desigualdades, tambi\u00e9n conocidas como inecuaciones, que son enunciados matem\u00e1ticos que se utilizan para comparar dos expresiones.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Daremos soluci\u00f3n a las desigualdades aplicando los procedimientos algebraicos necesarios y revisaremos su representaci\u00f3n gr\u00e1fica en el recta num\u00e9rica. Para dar m\u00e1s formalidad a la soluci\u00f3n explicaremos el procedimiento necesario para la obtenci\u00f3n del intervalo (conjunto de valores que cumplen con la desigualdad).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u00bfPara qu\u00e9 sirve una desigualdad?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Es una proposici\u00f3n que relaciona dos expresiones algebraicas cuyos valores son distintos. Los signos de expresi\u00f3n de las desigualdades matem\u00e1ticas se pueden sintetizar en la siguiente tabla.<\/p>\n\n\n\n<figure class=\"wp-block-table has-medium-font-size\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Menor que<\/td><td class=\"has-text-align-center\" data-align=\"center\">&lt;<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Mayor que<\/td><td class=\"has-text-align-center\" data-align=\"center\">&gt;<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Menor o igual que<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u2264<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Mayor o igual que<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u2265<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Verifica cu\u00e1l de los siguientes elementos del conjunto {-5,-2, 0, 4,} son soluciones de la desigualdad 3x &#8211; 2 &lt; 7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong>: Se sustituye cada valor en la desigualdad.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>a)<\/strong> Para<strong> x = -5<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>3( -5 ) &#8211; 2 &lt; 7<br>-15 &#8211; 2 &lt; 7<br>-17 &lt; 7<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><em>Desigualdad verdadera<\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>b)<\/strong> Para <strong>x = -2<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>3( -2 ) &#8211; 2 &lt; 7<br>-6 &#8211; 2 &lt; 7<br>-8 &lt; 7<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><em>Desigualdad verdadera<\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c)<\/strong> Para <strong>x = 0<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>3( 0 ) &#8211; 2 &lt; 7<br>0 &#8211; 2 &lt; 7<br>-2 &lt; 7<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><em>Desigualdad verdadera<\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c)<\/strong> Para <strong>x = 4<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>3( 4 ) &#8211; 2 &lt; 7<br>12 &#8211; 2 &lt; 7<br>10 &lt; 7<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><em>Desigualdad falsa<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">En este ejemplo los valores que hicieron verdadera la desigualdad, son soluciones de la expresi\u00f3n.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Propiedades de las desigualdades<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A continuaci\u00f3n se presentan las propiedades de las desigualdades y se cita un ejemplo para su comprensi\u00f3n.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-table has-medium-font-size\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Propiedad<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-table has-medium-font-size\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Ejemplo<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>a)<\/strong> Si los miembros de la expresi\u00f3n son multiplicados por el mismo valor, no cambia el signo de la desigualdad.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>4x &#8211; 2 &gt; 9<br>5(4x &#8211; 2) &gt; 5(9)<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>b) <\/strong>Si los miembros de la expresi\u00f3n son divididos por el mismo valor, el signo de la desigualdad no cambia.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-11.26.26.png\" alt=\"\" class=\"wp-image-1159\" width=\"162\" height=\"111\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-11.26.26.png\" alt=\"\" class=\"wp-image-1159\" width=\"162\" height=\"111\" \/><\/noscript><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c) <\/strong>Si los miembros de la expresi\u00f3n son sumados o restados por el mismo valor, el signo de la desigualdad no cambia.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>4x &#8211; 2 &gt; 9<br>4x &#8211; 2 &#8211; 3 &gt; 9 &#8211; 3<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>d) <\/strong>Si los miembros de la expresi\u00f3n son multiplicados por un n\u00famero negativo, el sentido de la desigualdad cambia de signo.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>(- 5)(4x &#8211; 2) &gt; ( &#8211; 5)(9)<br>(- 5)(4x &#8211; 2) &lt; (- 5)(9)<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>e) <\/strong>Si los miembros de la expresi\u00f3n son divididos por un valor negativo, el sentido de la desigualdad cambia de signo.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-11.29.47.png\" alt=\"\" class=\"wp-image-1160\" width=\"175\" height=\"118\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-11.29.47.png\" alt=\"\" class=\"wp-image-1160\" width=\"175\" height=\"118\" \/><\/noscript><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Intervalo de una desigualdad<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dados dos n\u00fameros cualesquiera <strong>a<\/strong> y <strong>b<\/strong>, tales que <strong>a &lt; b<\/strong> de la recta num\u00e9rica, se define intervalo de extremos <strong>a <\/strong>y <strong>b<\/strong> al conjunto de n\u00fameros reales comprendidos entre <strong>a <\/strong>y <strong>b<\/strong>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.37.39.png\" alt=\"\" class=\"wp-image-1189\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"701\" height=\"137\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.37.39.png\" alt=\"\" class=\"wp-image-1189\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.37.39.png 701w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.37.39-300x59.png 300w\" sizes=\"auto, (max-width: 701px) 100vw, 701px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\">Clasificaci\u00f3n de los intervalos<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">La clasificaci\u00f3n de los intervalos se muestra en la siguiente tabla, la cual servir\u00e1 como referencia para los ejercicios que m\u00e1s adelante resolveremos, donde <strong>a<\/strong> y <strong>b<\/strong> <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.39.09.png\" alt=\"\" class=\"wp-image-1190\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"66\" height=\"40\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.39.09.png\" alt=\"\" class=\"wp-image-1190\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">se lee, a y b elementos del conjunto de los n\u00fameros reales.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.54.51-1024x837.png\" alt=\"\" class=\"wp-image-1191\" width=\"800\" height=\"654\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.54.51-1024x837.png\" alt=\"\" class=\"wp-image-1191\" width=\"800\" height=\"654\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.54.51-1024x837.png 1024w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.54.51-300x245.png 300w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.54.51-768x628.png 768w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-14.54.51.png 1167w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Existen diferentes tipos de desigualdades y las que analizaremos en esta clase digital se denomina: desigualdad lineal con una variable.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Desigualdad lineal con una variable<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver una desigualdad lineal se debe despejar la inc\u00f3gnita para obtener todos los valores que satisfacen la desigualdad. A este conjunto de valores se le conoce como conjunto soluci\u00f3n. El conjunto soluci\u00f3n puede tener una, ninguna o una infinidad de soluciones.<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Resuelve la desigualdad <strong>3x + 9 &gt; 7x -3<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong>:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>a) <\/strong>Realizar el despeje necesario (dejar los t\u00e9rminos que contienen a la variable en un lado de la desigualdad y los t\u00e9rminos independientes en el otro lado de la desigualdad, aplicando reglas de signos).<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>3x + 9 &gt; 7x -3<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>3x &#8211; 7x &gt; -3 -9<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>b) <\/strong>Agrupar t\u00e9rminos semejantes.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>-4x &gt; -12<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c) <\/strong>Dividiendo entre <strong>-4<\/strong>, se aplica la propiedad de la desigualdad y el signo de dicha desigualdad cambia.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.04.12.png\" alt=\"\" class=\"wp-image-1192\" width=\"171\" height=\"71\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.04.12.png\" alt=\"\" class=\"wp-image-1192\" width=\"171\" height=\"71\" \/><\/noscript><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>d) <\/strong>Simplificar la desigualdad.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>x &lt; 3<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>f) <\/strong>El conjunto soluci\u00f3n ser\u00e1n todos los valores menores a 3 y esto lo podemos representar en forma de intervalo, utilizando la tabla 1, donde la desigualdad es del tipo: x &lt; a<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.06.00.png\" alt=\"\" class=\"wp-image-1193\" width=\"149\" height=\"64\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.06.00.png\" alt=\"\" class=\"wp-image-1193\" width=\"149\" height=\"64\" \/><\/noscript><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>g) <\/strong>Gr\u00e1fica (puede elegirse una de las dos gr\u00e1ficas)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.06.42.png\" alt=\"\" class=\"wp-image-1194\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"68\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.06.42.png\" alt=\"\" class=\"wp-image-1194\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.06.42.png 307w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.06.42-300x66.png 300w\" sizes=\"auto, (max-width: 307px) 100vw, 307px\" \/><\/noscript><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Determina el intervalo y gr\u00e1fica el conjunto soluci\u00f3n de la desigualdad: <strong>-10x &#8211; 1 &lt; -2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong>:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>a) <\/strong>Realizar el despeje necesario. A la desigualdad se le suma 1<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>-10 \u2264 x &#8211; 1 &lt; &#8211; 2<\/strong><br><strong>-10 + 1 \u2264 x -1 + 1 &lt; -2 +1<\/strong><br><strong>-9 \u2264 x &lt; -1<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>b) <\/strong>El conjunto soluci\u00f3n ser\u00e1n del tipo: a \u2264 x &lt; b, utilizando la tabla de desigualdades, se obtiene el intervalo.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>[-9,-1)<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c) <\/strong>Gr\u00e1fica (puede elegirse una de las dos gr\u00e1ficas)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.13.11.png\" alt=\"\" class=\"wp-image-1196\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"238\" height=\"90\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.13.11.png\" alt=\"\" class=\"wp-image-1196\" \/><\/noscript><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Para revisar m\u00e1s ejercicios referentes a desigualdades, te invito a que revises el siguiente link:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Inecuaciones de Primer Grado - Lineales | Ejemplo 1\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/CkVXbU-PNRs?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Desigualdad con valor absoluto<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">El conjunto soluci\u00f3n de una desigualdad que involucra valor absoluto, est\u00e1 dado por las siguientes propiedades :<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.15.39-1024x277.png\" alt=\"\" class=\"wp-image-1197\" width=\"891\" height=\"241\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.15.39-1024x277.png\" alt=\"\" class=\"wp-image-1197\" width=\"891\" height=\"241\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.15.39-1024x277.png 1024w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.15.39-300x81.png 300w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.15.39-768x208.png 768w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.15.39.png 1041w\" sizes=\"auto, (max-width: 891px) 100vw, 891px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Para resolver una desigualdad con valor absoluto, se llevan a cabo los siguientes pasos:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Verificar el tipo de desigualdad empleando la tabla de las propiedades de las desigualdades.<\/li><li>Representar las desigualdades que se generan a partir de la forma obtenida de la tabla de clasificaci\u00f3n de intervalos para las desigualdades.<\/li><li>Resolver cada desigualdad lineal.<\/li><li>Realizar una representaci\u00f3n gr\u00e1fica utilizando la tabla de clasificaci\u00f3n de intervalos para las desigualdades (cualquiera de las dos gr\u00e1ficas es v\u00e1lida).<\/li><li>Utilizar la tabla de clasificaci\u00f3n de intervalos para obtener el conjunto soluci\u00f3n.<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Determina el conjunto soluci\u00f3n para la desigualdad |x| \u2264 7<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.16.59-1024x711.png\" alt=\"\" class=\"wp-image-1198\" width=\"831\" height=\"577\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.16.59-1024x711.png\" alt=\"\" class=\"wp-image-1198\" width=\"831\" height=\"577\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.16.59-1024x711.png 1024w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.16.59-300x208.png 300w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.16.59-768x533.png 768w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-26-a-las-15.16.59.png 1236w\" sizes=\"auto, (max-width: 831px) 100vw, 831px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo: <\/strong>|2x + 3| \u2265 x +3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n: <\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/unnamed.png\" alt=\"\" class=\"wp-image-1199\" width=\"630\" height=\"618\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/unnamed.png\" alt=\"\" class=\"wp-image-1199\" width=\"630\" height=\"618\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/unnamed.png 512w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/unnamed-300x294.png 300w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Te compartimos el siguiente link donde podr\u00e1s interactuar con ejercicios que incluyen desigualdades con valor absoluto:<\/p>\n\n\n\n<div class=\"wp-block-buttons alignwide is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button aligncenter\"><a class=\"wp-block-button__link has-accent-background-color has-background\" href=\"http:\/\/prepa8.unam.mx\/academia\/colegios\/matematicas\/paginacolmate\/applets\/tsm\/Applets_Geogebra\/inecvalabs.html\" target=\"_blank\" rel=\"noreferrer noopener\">Inecuaciones con valor absoluto<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Conclusi\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En esta clase virtual revisamos el tema referente a las desigualdades, en donde se dio a conocer que son proposiciones que relacionan dos expresiones algebraicas cuyos signos son distintos. Se presentaron las propiedades de las desigualdades que son de suma importancia para resolver \u00e9stas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mencionamos que para dar soluci\u00f3n a una desigualdad, es necesario calcular el intervalo de valores que cumplen con dicha desigualdad. Existen varios tipos de intervalos: abierto, cerrado, semiabierto y semicerrado, el cual depender\u00e1 de la desigualdad resuelta. Asimismo, el conjunto soluci\u00f3n puede ser representado gr\u00e1ficamente (en esta clase se mencionan dos tipos de gr\u00e1ficos y cualquiera de ellos es v\u00e1lido).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente me es grato expresar que \u00a1has concluido la \u00faltima clase de este curso! Ha sido una gran experiencia compartir contigo este trayecto para tu formaci\u00f3n. Deseo que el curso haya cumplido con tus expectativas y te encuentres muy satisfecho con los temas revisados, as\u00ed como con tu desempe\u00f1o y compromiso.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Esperando encontrarte nuevamente, \u00a1\u00e9xito en lo que est\u00e1 por venir!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/www.youtube.com\/watch?v=p8NP1YjPY-E\" target=\"_blank\" rel=\"noreferrer noopener\">Inecuaciones con valor absoluto<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=4KY4yOOAPSg\" target=\"_blank\" rel=\"noreferrer noopener\">\u00bfQu\u00e9 es el valor absoluto?<\/a><\/li><li>Aguilar M\u00e1rquez, A., (2009), Matem\u00e1ticas simplificadas, (2da Ed.). Pearson Educaci\u00f3n.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Es momento de informarte que estamos en la recta final del m\u00f3dulo y te comento que en esta clase abordaremos el tema de desigualdades, tambi\u00e9n conocidas como inecuaciones, que son enunciados matem\u00e1ticos que se utilizan para comparar dos expresiones. Daremos soluci\u00f3n a las desigualdades aplicando los procedimientos algebraicos necesarios y revisaremos su representaci\u00f3n &#8230; <a title=\"Clase digital 6. Desigualdades\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/clase-digital-6-desigualdades\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 6. Desigualdades\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[20,29],"tags":[30,4,31],"class_list":["post-1155","post","type-post","status-publish","format-standard","hentry","category-bloque-3","category-matematicas-i","tag-beatriz-rubio-campos","tag-clase-digital","tag-neba04"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/posts\/1155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/comments?post=1155"}],"version-history":[{"count":5,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/posts\/1155\/revisions"}],"predecessor-version":[{"id":1201,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/posts\/1155\/revisions\/1201"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/media?parent=1155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/categories?post=1155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/tags?post=1155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}