{"id":1030,"date":"2022-05-25T20:07:33","date_gmt":"2022-05-25T20:07:33","guid":{"rendered":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/?p=1030"},"modified":"2022-05-25T20:07:34","modified_gmt":"2022-05-25T20:07:34","slug":"clase-digital-4-ecuaciones-de-primer-grado","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/clase-digital-4-ecuaciones-de-primer-grado\/","title":{"rendered":"Clase digital 4. Ecuaciones de primer grado"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" 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-1031\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/989124.jpg\" style=\"object-position:59% 43%\" data-object-fit=\"cover\" data-object-position=\"59% 43%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1280\" height=\"490\" class=\"wp-block-cover__image-background wp-image-1031\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/989124.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\/989124.jpg 1280w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/989124-300x115.jpg 300w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/989124-1024x392.jpg 1024w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/989124-768x294.jpg 768w\" 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\">Ecuaciones de primer grado<\/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\">Es un gusto saludarte, espero que te encuentres de lo mejor y avanzando en este m\u00f3dulo que hemos dise\u00f1ado con mucho entusiasmo para que sea de gran aprendizaje. En esta clase digital 4 revisaremos el tema de las ecuaciones de primer grado, una igualdad matem\u00e1tica con una o m\u00e1s inc\u00f3gnitas que recibe este nombre porque sus variables (llamadas tambi\u00e9n inc\u00f3gnitas) est\u00e1n elevadas a la primera potencia.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver la ecuaci\u00f3n lineal, previamente haremos una revisi\u00f3n sobre la metodolog\u00eda para encontrar su soluci\u00f3n, ya que \u00e9sta ser\u00e1 una herramienta \u00fatil. Asimismo, realizaremos una serie de ejercicios para diferentes tipos de ecuaciones de primer grado y analizaremos un caso particular: aquellas ecuaciones que involucran al valor absoluto, previamente definido el concepto. Finalmente, se presentan ejercicios de aplicaci\u00f3n que puedes encontrarte en la vida diaria. As\u00ed que \u00a1comencemos!<\/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\">Ecuaciones de primer grado<\/h3>\n\n\n\n<div class=\"wp-block-media-text alignwide has-media-on-the-right is-stacked-on-mobile\" style=\"grid-template-columns:auto 44%\"><figure class=\"wp-block-media-text__media\"><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-2022-05-25-a-las-11.34.10.png\" alt=\"\" class=\"wp-image-1033 size-full\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"691\" height=\"321\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-11.34.10.png\" alt=\"\" class=\"wp-image-1033 size-full\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-11.34.10.png 691w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-11.34.10-300x139.png 300w\" sizes=\"auto, (max-width: 691px) 100vw, 691px\" \/><\/noscript><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"wp-block-paragraph\" style=\"font-size:25px\">Una ecuaci\u00f3n de primer grado o ecuaci\u00f3n lineal es una igualdad algebraica cuya potencia es equivalente a uno, puede contener una, dos o m\u00e1s inc\u00f3gnitas.<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Reglas pr\u00e1cticas para resolver ecuaciones de primer grado<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver ecuaciones de primer grado, se aplica la transposici\u00f3n de t\u00e9rminos, que consiste en los siguientes puntos:<\/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-2022-05-25-a-las-11.35.35-1024x774.png\" alt=\"\" class=\"wp-image-1034\" width=\"902\" height=\"682\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-11.35.35-1024x774.png\" alt=\"\" class=\"wp-image-1034\" width=\"902\" height=\"682\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-11.35.35-1024x774.png 1024w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-11.35.35-300x227.png 300w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-11.35.35-768x580.png 768w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-11.35.35.png 1063w\" sizes=\"auto, (max-width: 902px) 100vw, 902px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\">Pasos para resolver una ecuaci\u00f3n de primer grado<\/h3>\n\n\n\n<ol class=\"wp-block-list\"><li>Quitar denominadores.<\/li><li>Quitar par\u00e9ntesis, realizando las operaciones necesarias.<\/li><li>Aplicar las reglas de transposici\u00f3n (dejar en alg\u00fan miembro todos los t\u00e9rminos con inc\u00f3gnita y en el otro miembro los t\u00e9rminos independientes).<\/li><li>Simplificar t\u00e9rminos semejantes.<\/li><li>Encontrar el valor de la soluci\u00f3n.<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Encuentre el valor de la inc\u00f3gnita en la ecuaci\u00f3n <em>y &#8211; 4 = 6.<\/em><\/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-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>a) <\/strong>Aplicar la regla de transposici\u00f3n, el -4 est\u00e1 restando, pasa sumando al segundo miembro de la ecuaci\u00f3n.<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>b) <\/strong>Simplificar la ecuaci\u00f3n sumando t\u00e9rminos semejantes y encontrar el valor de la inc\u00f3gnita<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong><em>y<\/em> &#8211; 4 = 6<br><em>y<\/em> = 6 + 4<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong><em>y<\/em> = 10<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Encuentre el valor de la inc\u00f3gnita en la ecuaci\u00f3n 3<em>w<\/em> &#8211; 3 = 4<em>w <\/em>+ 11<\/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-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>a) <\/strong>Aplicar la regla de transposici\u00f3n, dejando en el primer miembro los t\u00e9rminos con la inc\u00f3gnita y en el derecho los t\u00e9rminos independientes. <strong>-3<\/strong> est\u00e1 restando pasa sumando al segundo miembro de la ecuaci\u00f3n y <strong>4w<\/strong> est\u00e1 sumando pasa restando al primer miembro.<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>b) <\/strong>Simplificar la ecuaci\u00f3n sumando t\u00e9rminos semejantes.<\/p>\n\n\n\n<div style=\"height:9px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c)<\/strong> Multiplicar la ecuaci\u00f3n por -1 y encontrar la soluci\u00f3n.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>3w &#8211; 3 = 4w + 11<br>3w &#8211; 4w = 11 + 3<\/strong><\/p>\n\n\n\n<div style=\"height:42px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong><em>&#8211; w  = 14<\/em><\/strong><\/p>\n\n\n\n<div style=\"height:4px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>(- 1)( &#8211; w = 14)<br>w = &#8211; 14<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Resuelve la ecuaci\u00f3n 4 (x &#8211; 2) &#8211; 5 (x &#8211; 6) = 8 (x + 1) &#8211; 3 (2x + 3)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong>: En esta ecuaci\u00f3n es necesario quitar los par\u00e9ntesis realizando las operaciones necesarias.<\/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\" style=\"flex-basis:66.66%\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>a) <\/strong>Quitar par\u00e9ntesis realizando las operaciones necesarias.<\/p>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>b) <\/strong>Aplicar la regla de transposici\u00f3n de t\u00e9rmino.<\/p>\n\n\n\n<div style=\"height:22px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c)<\/strong> Simplificar la ecuaci\u00f3n sumando t\u00e9rminos semejantes.<\/p>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>d)<\/strong> Aplicar la regla para transposici\u00f3n de t\u00e9rminos. -3 est\u00e1 multiplicando, pasa dividiendo al segundo miembro.<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>e) <\/strong>Aplicar la regla para transposici\u00f3n de t\u00e9rminos. -3 est\u00e1 multiplicando, pasa dividiendo al segundo miembro.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<div style=\"height:7px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>4(x &#8211; 2) -5(x &#8211; 6) = 8(x+1)-3(2x + 3)<br>4x &#8211; 8 &#8211; 5x + 30 = 8x + 8 &#8211; 6x &#8211; 9<\/strong><\/p>\n\n\n\n<div style=\"height:2px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong><em>4x &#8211; 5x &#8211; 8x + 6x = 8 &#8211; 9 + 8 &#8211; 30<\/em><\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>10x &#8211; 13x = 16 &#8211; 39<br>-3x = &#8211; 23<\/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\/Captura-de-Pantalla-2022-05-25-a-las-13.55.35.png\" alt=\"\" class=\"wp-image-1086\" width=\"160\" height=\"93\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-13.55.35.png\" alt=\"\" class=\"wp-image-1086\" width=\"160\" height=\"93\" \/><\/noscript><\/figure>\n<\/div>\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\/Captura-de-Pantalla-2022-05-25-a-las-13.56.21.png\" alt=\"\" class=\"wp-image-1087\" width=\"145\" height=\"81\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-13.56.21.png\" alt=\"\" class=\"wp-image-1087\" width=\"145\" height=\"81\" \/><\/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>: Encuentra el valor de x en la ecuaci\u00f3n<\/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-2022-05-25-a-las-13.57.24.png\" alt=\"\" class=\"wp-image-1089\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"279\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-13.57.24.png\" alt=\"\" class=\"wp-image-1089\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong>: En esta ecuaci\u00f3n es necesario quitar denominadores, por lo que, se multiplica toda la ecuaci\u00f3n por el m\u00ednimo com\u00fan m\u00faltiplo (mcm).<\/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>Quitar denominadores, multiplicando toda la ecuaci\u00f3n por el mcm. En este caso el mcm es<strong> 6<\/strong> y se coloca un <strong>1 <\/strong>en el denominador para convertirlo en fracci\u00f3n, de igual manera para<strong> 10.<\/strong><\/p>\n\n\n\n<div style=\"height:53px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>b)<\/strong> Realizar las operaciones y simplificar.<\/p>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c) <\/strong>Aplicar la regla de transposici\u00f3n cuantas veces sea necesario y simplificar a su m\u00ednima expresi\u00f3n.<\/p>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>d)<\/strong> Encontrar la soluci\u00f3n para la ecuaci\u00f3n.<\/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-2022-05-25-a-las-13.59.30.png\" alt=\"\" class=\"wp-image-1090\" width=\"337\" height=\"155\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-13.59.30.png\" alt=\"\" class=\"wp-image-1090\" width=\"337\" height=\"155\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-13.59.30.png 420w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-13.59.30-300x138.png 300w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<div style=\"height:17px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image 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-2022-05-25-a-las-14.02.19.png\" alt=\"\" class=\"wp-image-1092\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"653\" height=\"87\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-14.02.19.png\" alt=\"\" class=\"wp-image-1092\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-14.02.19.png 653w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-14.02.19-300x40.png 300w\" sizes=\"auto, (max-width: 653px) 100vw, 653px\" \/><\/noscript><\/figure>\n\n\n\n<div style=\"height:13px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\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\/Captura-de-Pantalla-2022-05-25-a-las-14.03.14.png\" alt=\"\" class=\"wp-image-1093\" width=\"295\" height=\"196\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-14.03.14.png\" alt=\"\" class=\"wp-image-1093\" width=\"295\" height=\"196\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-14.03.14.png 349w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-14.03.14-300x199.png 300w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-14.03.14-272x182.png 272w\" sizes=\"auto, (max-width: 295px) 100vw, 295px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center wp-block-paragraph\" style=\"font-size:25px\"><strong>X = 15<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Ecuaciones de primer grado con valor absoluto<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Para poder dar soluci\u00f3n a una ecuaci\u00f3n con valor absoluto, primero es importante saber qu\u00e9 es el valor absoluto de un n\u00famero.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Valor absoluto de un n\u00famero<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El valor absoluto de un n\u00famero es la distancia que existe desde cero al n\u00famero indicado en una recta num\u00e9rica, El valor absoluto es un n\u00famero sin signo y se representa matem\u00e1ticamente encerrando al n\u00famero entre dos l\u00edneas paralelas. <strong>El valor de un n\u00famero negativo o positivo siempre dar\u00e1 como resultado un n\u00famero positivo.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>|5| = 5<br>|- 9| = 9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo que podemos generalizar que para resolver una ecuaci\u00f3n con valor absoluto se tiene |x| = a, su soluci\u00f3n est\u00e1 dada por:<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\">x = a <strong>y<\/strong><br>x = &#8211; a<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Resuelve la ecuaci\u00f3n |x + 1| = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong>: Se aplica la definici\u00f3n de valor absoluto y se obtienen dos ecuaciones.<\/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> Resolver cada una de las ecuaciones<\/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>&#8211; (x + 1) = 8<\/strong><br><strong>&#8211; x &#8211; 1 = 8<\/strong><\/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 + 1 = 8<\/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> Aplicar transposici\u00f3n de t\u00e9rminos.<\/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>&#8211; x = 8 + 1<\/strong><\/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 = 8 &#8211; 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-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>c)<\/strong> Encontrar el valor de la inc\u00f3gnita.<\/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\">&#8211; <strong>x = 9<br>(- 1)(- x = 9)<br>x = &#8211; 9<\/strong><\/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 = 7<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">El conjunto soluci\u00f3n se expresa como: {-9, 7}.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En la pr\u00e1ctica, nos encontramos con situaciones reales que se pueden presentar en la vida diaria y que pueden ser resueltas encontrando el valor de la inc\u00f3gnita. A continuaci\u00f3n te presentamos un ejemplo de aplicaci\u00f3n.<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>Ejemplo<\/strong>: Si dentro de 15 a\u00f1os Olivia tiene el doble de edad que la que ten\u00eda hace 5 a\u00f1os, \u00bfqu\u00e9 edad tiene ahora?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Datos<\/th><th class=\"has-text-align-center\" data-align=\"center\">Dentro de 15 a\u00f1os<\/th><th class=\"has-text-align-center\" data-align=\"center\">Planteamiento<\/th><\/tr><\/thead><tbody><tr><td>Edad de Olivia: x<\/td><td class=\"has-text-align-center\" data-align=\"center\">x + 15<br>2 (x &#8211; 5)<\/td><td class=\"has-text-align-center\" data-align=\"center\">x + 5 = 2(x- 5)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Resolvemos la ecuaci\u00f3n:<\/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-2022-05-25-a-las-15.05.33-1024x130.png\" alt=\"\" class=\"wp-image-1123\" width=\"803\" height=\"102\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-15.05.33-1024x130.png\" alt=\"\" class=\"wp-image-1123\" width=\"803\" height=\"102\" srcset=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-15.05.33-1024x130.png 1024w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-15.05.33-300x38.png 300w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-15.05.33-768x97.png 768w, https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-content\/uploads\/sites\/69\/2022\/05\/Captura-de-Pantalla-2022-05-25-a-las-15.05.33.png 1072w\" sizes=\"auto, (max-width: 803px) 100vw, 803px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">La edad de Olivia es de 25 a\u00f1os.<\/p>\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 analizamos la metodolog\u00eda para resolver ecuaciones de primer grado o ecuaciones lineales, donde el exponente de la variable es 1. Existe una gran diversidad de ecuaciones de primer grado como: fraccionarias, con signos de agrupaci\u00f3n o par\u00e9ntesis, con valor absoluto, por solo mencionar algunas de ellas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El valor absoluto de un n\u00famero ser\u00e1 la distancia que existe del valor al origen y se representa por medio de dos barras paralelas, obteni\u00e9ndose un valor positivo, ya sea de un n\u00famero positivo o negativo. La aplicaci\u00f3n de las ecuaciones de primer grado es muy extensa, pues por medio del planteamiento utilizando el lenguaje algebraico se obtiene la ecuaci\u00f3n para ser resuelta.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Y es as\u00ed, como damos por finalizada una clase virtual, m\u00e1s. Te invito a que contin\u00faes porque estamos en la recta final.<\/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.superprof.es\/apuntes\/escolar\/matematicas\/algebra\/ecuaciones\/ecuaciones-de-primer-grado.html\">Ecuaciones de primer grado: saberlo todo<\/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 Es un gusto saludarte, espero que te encuentres de lo mejor y avanzando en este m\u00f3dulo que hemos dise\u00f1ado con mucho entusiasmo para que sea de gran aprendizaje. En esta clase digital 4 revisaremos el tema de las ecuaciones de primer grado, una igualdad matem\u00e1tica con una o m\u00e1s inc\u00f3gnitas que recibe este nombre &#8230; <a title=\"Clase digital 4. Ecuaciones de primer grado\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/clase-digital-4-ecuaciones-de-primer-grado\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 4. Ecuaciones de primer grado\">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-1030","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\/1030","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=1030"}],"version-history":[{"count":12,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/posts\/1030\/revisions"}],"predecessor-version":[{"id":1124,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/posts\/1030\/revisions\/1124"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/media?parent=1030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/categories?post=1030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/bachilleratovirtual\/wp-json\/wp\/v2\/tags?post=1030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}