{"id":4603,"date":"2022-01-14T21:01:26","date_gmt":"2022-01-14T21:01:26","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=4603"},"modified":"2022-02-08T18:59:34","modified_gmt":"2022-02-08T18:59:34","slug":"clase-digital-2-propiedades-de-desigualdades-resolucion-de-desigualdades-de-primer-y-segundo-orden","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-2-propiedades-de-desigualdades-resolucion-de-desigualdades-de-primer-y-segundo-orden\/","title":{"rendered":"Clase digital 2: Propiedades de desigualdades, resoluci\u00f3n de desigualdades de primer y segundo orden"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-4606\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck.jpg\" style=\"object-position:59% 64%\" data-object-fit=\"cover\" data-object-position=\"59% 64%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1067\" class=\"wp-block-cover__image-background wp-image-4606\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck.jpg\" style=\"object-position:59% 64%\" data-object-fit=\"cover\" data-object-position=\"59% 64%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-1024x683.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-1536x1024.jpg 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-272x182.jpg 272w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/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\">Propiedades de desigualdades, resoluci\u00f3n de desigualdades de primer y segundo orden<\/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!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es un gusto encontrarte nuevamente, espero que est\u00e9s aprendiendo mucho, sobre todo, que tu \u00e1nimo no decaiga y sigas conociendo m\u00e1s acerca de los temas que se te presentan. Por lo tanto te invito a continuar en la segunda clase denominada Propiedades de desigualdades, resoluci\u00f3n de desigualdades de primer y segundo orden del curso de <strong>C\u00e1lculo Diferencial<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En esta segunda clase se abordar\u00e1 la resoluci\u00f3n de desigualdades de primer y segundo grado, as\u00ed como desigualdades de valor absoluto, las desigualdades permiten plantear problemas de aplicaci\u00f3n y resolverse. Ser\u00e1s capaz de resolver problemas de aplicaci\u00f3n adem\u00e1s de plantear la desigualdad.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente, recuerda que lo importante es que logres aprender lo mejor posible.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Te deseo much\u00edsimo \u00e9xito!<\/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\" id=\"desigualdades-y-sus-propiedades\">Desigualdades y sus propiedades<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">El conjunto de los n\u00fameros reales es un conjunto ordenado y se pueden establecer relaciones de orden entre dos n\u00fameros como: 52&lt;6, 1&gt;-4, 6\u226420, a estas expresiones se les llaman desigualdades.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\" id=\"tipo-de-desigualdades\">Tipo de desigualdades<\/h5>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Desigualdades estrictas<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Se lee<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">a&lt;b<\/td><td class=\"has-text-align-left\" data-align=\"left\">a es menor que b<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">a&gt;b<\/td><td class=\"has-text-align-left\" data-align=\"left\">a es mayor que b<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Desigualdades no estrictas<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\"><strong>Se lee<\/strong><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><em>a\u2264b<\/em><\/td><td class=\"has-text-align-left\" data-align=\"left\">a es menor o igual que b<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><em>a\u2265b<\/em><\/td><td class=\"has-text-align-left\" data-align=\"left\">a es mayor o igual que b<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"desigualdad\">Desigualdad<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Una desigualdad es una expresi\u00f3n matem\u00e1tica que involucra variables, constantes y cualquiera de los s\u00edmbolos&nbsp;&lt;,\u2264,&gt; o\u2265.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por resolver una desigualdad se entiende determinar el intervalo o combinaci\u00f3n de intervalos (de n\u00fameros reales) cuyos elementos satisfacen la desigualdad.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo&nbsp;<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Encuentra el conjunto de valores para x que hacen verdadera la desigualdad&nbsp;x &#8211; 3 &gt; 10 y representa la soluci\u00f3n en notaci\u00f3n de intervalo y en la recta num\u00e9rica.<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicando la propiedad aditiva de los n\u00fameros reales. Sumando +3 en ambos lados de la desigualdad<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-14.59.14.png\" alt=\"\" class=\"wp-image-4630\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"134\" height=\"41\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-14.59.14.png\" alt=\"\" class=\"wp-image-4630\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Representado en notaci\u00f3n de intervalo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.00.47.png\" alt=\"\" class=\"wp-image-4631\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"101\" height=\"39\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.00.47.png\" alt=\"\" class=\"wp-image-4631\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Representando en la recta num\u00e9rica<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.01.12.png\" alt=\"\" class=\"wp-image-4632\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"459\" height=\"82\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.01.12.png\" alt=\"\" class=\"wp-image-4632\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.01.12.png 459w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.01.12-300x54.png 300w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h5 class=\"wp-block-heading\" id=\"comprobacion\">Comprobaci\u00f3n<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">Para verificar que el conjunto soluci\u00f3n es correcto, se sugiere elegir cualquier valor y sustituirlo en la desigualdad, al ser una desigualdad estricta no se puede elegir el n\u00famero 13, por tanto, se elige el 14.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sustituyendo 14 en la desigualdad<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">14 &#8211; 3 &gt; 10<br>11 &gt; 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">11 es mayor que 10 por lo tanto la proposici\u00f3n es verdadera.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Encuentre el conjunto soluci\u00f3n a la desigualdad&nbsp;10 &#8211; 8x &lt; 4x &#8211; 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n anal\u00edtica<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Utilizando la propiedad aditiva para tener del lado izquierdo la variable y del lado derecho los valores independientes.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">-8x &#8211; 4x &lt; 10 &#8211; 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sumando&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">-12x &lt; 9<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.03.39.png\" alt=\"\" class=\"wp-image-4637\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"634\" height=\"100\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.03.39.png\" alt=\"\" class=\"wp-image-4637\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.03.39.png 634w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.03.39-300x47.png 300w\" sizes=\"auto, (max-width: 634px) 100vw, 634px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto el conjunto soluci\u00f3n es<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.04.21.png\" alt=\"\" class=\"wp-image-4640\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"123\" height=\"34\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.04.21.png\" alt=\"\" class=\"wp-image-4640\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">3. Encuentra el conjunto soluci\u00f3n de la desigualdad<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.04.49.png\" alt=\"\" class=\"wp-image-4641\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"164\" height=\"32\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.04.49.png\" alt=\"\" class=\"wp-image-4641\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">expresa en la soluci\u00f3n en notaci\u00f3n de conjunto de intervalo y representa en la recta num\u00e9rica.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.05.19.png\" alt=\"\" class=\"wp-image-4643\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"166\" height=\"57\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.05.19.png\" alt=\"\" class=\"wp-image-4643\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Multiplicando por 1\/2<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.06.26.png\" alt=\"\" class=\"wp-image-4644\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"159\" height=\"56\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.06.26.png\" alt=\"\" class=\"wp-image-4644\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicando la propiedad aditiva<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.06.48.png\" alt=\"\" class=\"wp-image-4645\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"131\" height=\"52\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.06.48.png\" alt=\"\" class=\"wp-image-4645\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Reduciendo t\u00e9rminos<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.07.12.png\" alt=\"\" class=\"wp-image-4646\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"109\" height=\"43\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.07.12.png\" alt=\"\" class=\"wp-image-4646\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicar la propiedad multiplicativa y la desigualdad cambia. Multiplicando por -3<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.07.50.png\" alt=\"\" class=\"wp-image-4647\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"644\" height=\"153\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.07.50.png\" alt=\"\" class=\"wp-image-4647\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.07.50.png 644w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.07.50-300x71.png 300w\" sizes=\"auto, (max-width: 644px) 100vw, 644px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">4. Encuentra el conjunto de la desigualdad<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.08.23.png\" alt=\"\" class=\"wp-image-4648\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"109\" height=\"58\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.08.23.png\" alt=\"\" class=\"wp-image-4648\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Multiplicando por 4<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">-8 &lt; 6 &#8211; 2x\u226420<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Planteando dos desigualdades y resolviendo cada una<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.09.56.png\" alt=\"\" class=\"wp-image-4649\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"689\" height=\"212\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.09.56.png\" alt=\"\" class=\"wp-image-4649\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.09.56.png 689w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.09.56-300x92.png 300w\" sizes=\"auto, (max-width: 689px) 100vw, 689px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"desigualdad-de-segundo-grado\">Desigualdad de segundo grado<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Una desigualdad de segundo grado en la variable x en su forma simple es&nbsp;<em>ax<sup>2<\/sup> + bx + c &lt; 0<\/em>, la expresi\u00f3n tambi\u00e9n es v\u00e1lida para los s\u00edmbolos &gt;,\u2264,\u2265.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La soluci\u00f3n de una desigualdad de segundo grado tiene tres casos de soluci\u00f3n:&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Dos ra\u00edces reales<\/li><li>Una ra\u00edz real<\/li><li>Ra\u00edces complejas<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Encuentra el conjunto soluci\u00f3n de la desigualdad x<sup>2<\/sup> &#8211; 3x + 2 &gt; 0.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizando la desigualdad<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">(x-2) (x-1) &gt; 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Obteniendo puntos cr\u00edticos<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.12.00.png\" alt=\"\" class=\"wp-image-4653\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"106\" height=\"107\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.12.00.png\" alt=\"\" class=\"wp-image-4653\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Dibuja en la recta num\u00e9rica los puntos cr\u00edticos y traza l\u00edneas verticales que dividen la recta.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.12.30.png\" alt=\"\" class=\"wp-image-4654\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"477\" height=\"137\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.12.30.png\" alt=\"\" class=\"wp-image-4654\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.12.30.png 477w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.12.30-300x86.png 300w\" sizes=\"auto, (max-width: 477px) 100vw, 477px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Elegir valores entre esos segmentos y comprobar que la desigualdad se cumpla.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Elegir un valor entre&nbsp;-\u221e y 1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.12.59.png\" alt=\"\" class=\"wp-image-4657\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"181\" height=\"114\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.12.59.png\" alt=\"\" class=\"wp-image-4657\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se cumple la desigualdad, por lo tanto un conjunto soluci\u00f3n es&nbsp;<em>S = (-\u221e, 1)<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Elegir el siguiente valor entre 1 y 2.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.13.42.png\" alt=\"\" class=\"wp-image-4658\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"189\" height=\"107\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.13.42.png\" alt=\"\" class=\"wp-image-4658\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La desigualdad no se cumple por lo tanto no hay soluci\u00f3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Elegir un valor entre&nbsp;2 y \u221e.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.14.16.png\" alt=\"\" class=\"wp-image-4660\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"96\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.14.16.png\" alt=\"\" class=\"wp-image-4660\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se cumple la desigualdad, por lo tanto un conjunto soluci\u00f3n es&nbsp;S = (2,\u221e)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto la soluci\u00f3n es S=(-\u221e,1) \u222a (2,\u221e)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Resuelve la desigualdad <em>4\u2264x<sup>2<\/sup><\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reescribiendo la desigualdad<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.15.27.png\" alt=\"\" class=\"wp-image-4663\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"48\" height=\"35\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.15.27.png\" alt=\"\" class=\"wp-image-4663\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sacando ra\u00edz cuadrada<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.15.52.png\" alt=\"\" class=\"wp-image-4664\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"67\" height=\"32\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.15.52.png\" alt=\"\" class=\"wp-image-4664\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto los puntos cr\u00edticos son&nbsp;x = -2 y x = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Elegir tres puntos cr\u00edticos entre -\u221e a-2; -2 a 2 y 2 a \u221e<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.16.49.png\" alt=\"\" class=\"wp-image-4667\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"82\" height=\"91\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.16.49.png\" alt=\"\" class=\"wp-image-4667\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Al cumplirse la desigualdad un conjunto soluci\u00f3n es<\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.17.28.png\" alt=\"\" class=\"wp-image-4670\" width=\"118\" height=\"34\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.17.28.png\" alt=\"\" class=\"wp-image-4670\" width=\"118\" height=\"34\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.17.39.png\" alt=\"\" class=\"wp-image-4672\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"62\" height=\"79\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.17.39.png\" alt=\"\" class=\"wp-image-4672\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">No se cumple la desigualdad por tanto el conjunto (-2,2) no es soluci\u00f3n.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.18.31.png\" alt=\"\" class=\"wp-image-4674\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"84\" height=\"86\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.18.31.png\" alt=\"\" class=\"wp-image-4674\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Al cumplirse la desigualdad un conjunto soluci\u00f3n es&nbsp;S = [2,\u221e)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto el conjunto soluci\u00f3n es&nbsp;S = (-\u221e,-2]\u222a [2,\u221e)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"desigualdades-racionales\">Desigualdades racionales<\/h4>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.19.37.png\" alt=\"\" class=\"wp-image-4678\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"772\" height=\"53\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.19.37.png\" alt=\"\" class=\"wp-image-4678\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.19.37.png 772w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.19.37-300x21.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.19.37-768x53.png 768w\" sizes=\"auto, (max-width: 772px) 100vw, 772px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Encuentra el conjunto soluci\u00f3n<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.20.14.png\" alt=\"\" class=\"wp-image-4680\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"56\" height=\"37\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.20.14.png\" alt=\"\" class=\"wp-image-4680\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reescribiendo la desigualdad<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.20.39.png\" alt=\"\" class=\"wp-image-4681\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"92\" height=\"51\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.20.39.png\" alt=\"\" class=\"wp-image-4681\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Realizando la operaci\u00f3n<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.21.05.png\" alt=\"\" class=\"wp-image-4682\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"103\" height=\"93\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.21.05.png\" alt=\"\" class=\"wp-image-4682\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Como el polinomio p(x) debe ser diferente de cero encontrar el punto cr\u00edtico, tomando el polinomio e igualarlo a cero.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">x-3 = 0<br>x = 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Resolver la parte lineal de la ecuaci\u00f3n&nbsp;-7x + 24 \u2264 0<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.22.02.png\" alt=\"\" class=\"wp-image-4686\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"96\" height=\"60\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.22.02.png\" alt=\"\" class=\"wp-image-4686\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Entonces los puntos cr\u00edticos son<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.22.49.png\" alt=\"\" class=\"wp-image-4689\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"113\" height=\"55\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.22.49.png\" alt=\"\" class=\"wp-image-4689\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">para encontrar el conjunto soluci\u00f3n elegir valores entre:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.23.15.png\" alt=\"\" class=\"wp-image-4690\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"208\" height=\"62\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.23.15.png\" alt=\"\" class=\"wp-image-4690\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Eligiendo x=0<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.23.43.png\" alt=\"\" class=\"wp-image-4693\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"429\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.23.43.png\" alt=\"\" class=\"wp-image-4693\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.23.43.png 429w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.23.43-300x66.png 300w\" sizes=\"auto, (max-width: 429px) 100vw, 429px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Eligiendo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.24.11.png\" alt=\"\" class=\"wp-image-4695\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"69\" height=\"57\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.24.11.png\" alt=\"\" class=\"wp-image-4695\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.24.15.png\" alt=\"\" class=\"wp-image-4696\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"119\" height=\"119\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.24.15.png\" alt=\"\" class=\"wp-image-4696\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">No se cumple la desigualdad por tanto ese conjunto no es soluci\u00f3n.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Eligiendo x=5<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.24.52.png\" alt=\"\" class=\"wp-image-4698\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"437\" height=\"100\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.24.52.png\" alt=\"\" class=\"wp-image-4698\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.24.52.png 437w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.24.52-300x69.png 300w\" sizes=\"auto, (max-width: 437px) 100vw, 437px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">El conjunto soluci\u00f3n es<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.25.20.png\" alt=\"\" class=\"wp-image-4699\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"40\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.25.20.png\" alt=\"\" class=\"wp-image-4699\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Recuerde que 3 no se puede tocar porque es el valor que hace cero p(x).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"desigualdad-de-valor-absoluto\">Desigualdad de valor absoluto<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Propiedades de las desigualdades de valor absoluto.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.26.08.png\" alt=\"\" class=\"wp-image-4702\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"622\" height=\"235\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.26.08.png\" alt=\"\" class=\"wp-image-4702\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.26.08.png 622w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.26.08-300x113.png 300w\" sizes=\"auto, (max-width: 622px) 100vw, 622px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Resuelve la desigualdad&nbsp;|x &#8211; 4| &lt; 30<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Identificando la propiedad la cual es 1, reescribiendo<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">-30 &lt; x &#8211; 4 &lt; 30<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Resolviendo la desigualdad<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">-26 &lt; x &lt; 34<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El conjunto soluci\u00f3n es S = (-26, 34)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Resuelve la desigualdad |-2x + 17| \u226510<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Identificando la propiedad la cual es 2, reescribiendo&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.28.01.png\" alt=\"\" class=\"wp-image-4706\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"287\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.28.01.png\" alt=\"\" class=\"wp-image-4706\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Resolviendo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.28.27.png\" alt=\"\" class=\"wp-image-4708\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"453\" height=\"170\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.28.27.png\" alt=\"\" class=\"wp-image-4708\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.28.27.png 453w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.28.27-300x113.png 300w\" sizes=\"auto, (max-width: 453px) 100vw, 453px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En resumen, las relaciones de orden entre dos n\u00fameros pertenecientes al conjunto de n\u00fameros reales se llaman desigualdades, estas expresiones matem\u00e1ticas involucran variables, constantes y cualquiera de los s\u00edmbolos &lt;, \u2264, &gt; o \u2265. Las desigualdades pueden ser de tipo estricto o no estricto.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Al determinar el intervalo o combinaci\u00f3n de intervalos (de n\u00fameros reales) cuyos elementos satisfacen una desigualdad podemos decir que se ha encontrado soluci\u00f3n a la desigualdad.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una desigualdad de segundo grado en la variable x puede tener tres casos de soluci\u00f3n: dos ra\u00edces reales, una ra\u00edz real o ra\u00edces complejas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una desigualdad racional es una expresi\u00f3n algebraica de la forma<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.29.10.png\" alt=\"\" class=\"wp-image-4709\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"64\" height=\"38\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Captura-de-Pantalla-2022-01-14-a-las-15.29.10.png\" alt=\"\" class=\"wp-image-4709\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">donde p(x) y q(x) son polinomios y q(x)\u22600. Para encontrar soluci\u00f3n a una desigualdad de valor absoluto es importante identificar las propiedades de las desigualdades de valor absoluto.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es as\u00ed como concluimos nuestra segunda clase. \u00a1Vas avanzando muy bien, te felicito! No olvides que para concluir la sesi\u00f3n debes hacer la tarea asignada y enviarla de manera correcta. Te encuentro en la siguiente clase, hasta luego.<\/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=\"http:\/\/recursostic.educacion.es\/secundaria\/edad\/4esomatematicasB\/inecuaciones\/impresos\/quincena5.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/recursostic.educacion.es\/secundaria\/edad\/4esomatematicasB\/inecuaciones\/impresos\/quincena5.pdf<\/a><\/li><li>Zill, D. G., &amp; Wrigth. W. S. (2011). <em>Matem\u00e1ticas 1: C\u00e1lculo Diferencial.<\/em> M\u00e9xico: MC Graw Hill.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Es un gusto encontrarte nuevamente, espero que est\u00e9s aprendiendo mucho, sobre todo, que tu \u00e1nimo no decaiga y sigas conociendo m\u00e1s acerca de los temas que se te presentan. Por lo tanto te invito a continuar en la segunda clase denominada Propiedades de desigualdades, resoluci\u00f3n de desigualdades de primer y segundo orden del &#8230; <a title=\"Clase digital 2: Propiedades de desigualdades, resoluci\u00f3n de desigualdades de primer y segundo orden\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-2-propiedades-de-desigualdades-resolucion-de-desigualdades-de-primer-y-segundo-orden\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 2: Propiedades de desigualdades, resoluci\u00f3n de desigualdades de primer y segundo orden\">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":[10,12],"tags":[41,149,44],"class_list":["post-4603","post","type-post","status-publish","format-standard","hentry","category-ingenieria-civil","category-uda-calculo-diferencial","tag-clase-digital","tag-marcela-guadalupe-tellez-martinez","tag-neli04036"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4603","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=4603"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4603\/revisions"}],"predecessor-version":[{"id":6954,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4603\/revisions\/6954"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=4603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=4603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=4603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}