{"id":2174,"date":"2019-11-07T18:31:28","date_gmt":"2019-11-07T18:31:28","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=2174"},"modified":"2019-11-13T21:07:43","modified_gmt":"2019-11-13T21:07:43","slug":"ecuacion-lineal-con-una-incognita","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=2174","title":{"rendered":"Ecuaci\u00f3n lineal con una inc\u00f3gnita"},"content":{"rendered":"\n<p><strong>Igualdad<\/strong>, expresi\u00f3n de que dos cantidades o expresiones algebraicas tienen el mismo Valor.<\/p>\n\n\n\n<p><strong>Ecuaci\u00f3n<\/strong>, igualdad donde hay cantidades desconocidas llamadas <strong>inc\u00f3gnitas<\/strong>, quienes son representadas por las \u00faltimas letras del alfabeto: x, y, z, u, v, Ejemplo:<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size\"><strong>5x + 2 =17<\/strong><\/p>\n\n\n\n<!--more-->\n\n\n\n<p>donde, el valor de x=3, si sustitu\u00edmos, se verificar\u00e1 la igualdad presentada<\/p>\n\n\n\n<blockquote class=\"wp-block-quote has-text-align-center is-style-default is-layout-flow wp-block-quote-is-layout-flow\"><p><strong>5(3) + 2 = 17<\/strong><\/p><p><strong> 17 = 17 <\/strong><\/p><\/blockquote>\n\n\n\n<p class=\"has-text-color has-luminous-vivid-orange-color\"><strong>Clases<\/strong><\/p>\n\n\n\n<p>Una <strong>Ecuaci\u00f3n num\u00e9rica<\/strong>, es una ecuaci\u00f3n que no tiene m\u00e1s letras que las inc\u00f3gnitas Ejem.: <strong>4x &#8211; 5 =x + 4<\/strong><\/p>\n\n\n\n<p>Una <strong>Ecuaci\u00f3n lineal<\/strong>, es una ecuaci\u00f3n que adem\u00e1s de las inc\u00f3gnitas, tiene otras letras, Ejem.: <strong>3x + 2a = 5b &#8211; bx<\/strong><\/p>\n\n\n\n<p>El <strong>Grado <\/strong>de una ecuaci\u00f3n con una sola inc\u00f3gnita es el mayor exponente que tiene la inc\u00f3gnita en la ecuaci\u00f3n, Ejem: <strong>4x &#8211; 6 = 3x &#8211; 1<\/strong> y <strong>ax + b =b<sup>2<\/sup>x + c<\/strong> son ecuaciones de <strong>Primer grado<\/strong>, <strong>x<\/strong><sup><strong>2<\/strong><\/sup><strong> -5x + 6 = 0<\/strong> es una ecuaci\u00f3n de <strong>Segundo grado<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p><strong>Resolver una ecuaci\u00f3n<\/strong>, es hallar sus ra\u00edces, o sea, el valor o los valores de las inc\u00f3gnitas que satisfacen la ecuaci\u00f3n.<\/p><\/blockquote>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-luminous-vivid-orange-color\"><strong>Ejemplo:<\/strong><\/p>\n\n\n\n<p>Resolver la ecuaci\u00f3n: <strong>3x &#8211; 5 = x + 3<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Pasar x al primer miembro y -5 al segundo, <\/li><li>Cambi\u00e1ndoles los signos, nos queda:<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>3x &#8211; x = 3 + 5<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>reduciendo los t\u00e9rminos:<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>2x = 8<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Finalmente, despejando x, tenemos:<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>x =<sup>8<\/sup>\u2044<sub>2<\/sub><\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>x = 4<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-background has-medium-font-size has-very-light-gray-color has-vivid-red-background-color\"><strong>Ejercicios:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_130718-scaled.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"323\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_130718-1024x323.jpg\" alt=\"\" class=\"wp-image-2179\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_130718-1024x323.jpg 1024w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_130718-300x95.jpg 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_130718-768x242.jpg 768w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_130718-1536x485.jpg 1536w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_130718-2048x646.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-vivid-cyan-blue-color\"><strong>Ejemplos de la aplicaci\u00f3n de las ecuaciones de primer grado:<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-vivid-red-color\"><strong>Ejemplo 1<\/strong><\/p>\n\n\n\n<p>La suma de las edades de A y B es de 84, y B tiene 8 a\u00f1os menos que A. Hallar ambas edades.<\/p>\n\n\n\n<p>sea x = la edad de A<\/p>\n\n\n\n<p>y como B tiene 8 a\u00f1os menos que A, determinamos que: x &#8211; 8=edad de B,<\/p>\n\n\n\n<p>la suma de ambas edades es de 84, entonces:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>x + x &#8211; 8 = 84<\/strong><\/p>\n\n\n\n<p>Resolviendo:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote has-text-align-center is-layout-flow wp-block-quote-is-layout-flow\"><p><strong>x + x = 84 + 8<\/strong><\/p><p><strong>2x = 92<\/strong><\/p><p><strong>x =  <sup>92<\/sup>\u2044<sub>2<\/sub><\/strong> = <strong>46 a\u00f1os de A<\/strong><\/p><p>La edad de <strong>B<\/strong>, ser\u00eda: x &#8211; 8 = 46 &#8211; 8 = <strong>38 a\u00f1os<\/strong> <\/p><\/blockquote>\n\n\n\n<p class=\"has-text-color has-vivid-red-color\"><strong>Ejemplo 2<\/strong><\/p>\n\n\n\n<p>Pague $87 por un libro, un traje y un sombrero. el sombrero costo $5 m\u00e1s que el libro y $20 menos que el traje, \u00bfcu\u00e1nto pagu\u00e9 por cada cosa?<\/p>\n\n\n\n<p>sea x = precio del libro.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>como el sombrero cost\u00f3 5 m\u00e1s que el libro: x + 5 = precio del sombrero.<\/li><li>el sombrero cost\u00f3 $20 menos que el traje, en otras palabras, el traje cuesta $20 mas que el sombrero:<\/li><li>(x + 5) + 20 = costo del traje<ul><li> RECORDEMOS QUE: (x+5) es el costo del sombrero<\/li><li>entonces x + 5 + 20 = costo del traje<\/li><li>quedar\u00eda x + 25 = costo del traje<\/li><\/ul><\/li><li>tenemos que el Libro, el Sombrero y el Traje, suman 87:<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>x + (x+5) + (x+25) = 87<\/strong><\/p>\n\n\n\n<p>quitando los par\u00e9ntesis: <strong>x + x + 5 + x + 25 = 87<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>3x + 30 = 87<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>3x = 87 &#8211; 30<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>3x = 57<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>x =  <sup>57<\/sup>\u2044<sub>3<\/sub> = $19 <\/strong>es el precio del libro<\/p>\n\n\n\n<p class=\"has-text-align-center\">x + 5 = 19 + 5 = <strong>$24<\/strong>, es el precio del sombrero<\/p>\n\n\n\n<p class=\"has-text-align-center\">x + 25 = 19 + 25 = <strong>$44<\/strong>, precio del traje<\/p>\n\n\n\n<p class=\"has-text-color has-vivid-red-color\"><strong>Ejemplo 3:<\/strong><\/p>\n\n\n\n<p>La suma de 3 n\u00fameros enteros consecutivos es de 156. Hallar esos n\u00fameros.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>x = n\u00famero menor<\/li><li>x+1 = n\u00famero intermedio<\/li><li>x+2 = n\u00famero mayor<\/li><li>la suma del N\u00famero menor, el Intermedio y el Mayo es 156:<ul><li>x + (x+1) + (x+2) = 156<\/li><\/ul><\/li><li>quitando los par\u00e9ntesis:<ul><li>x + x + 1 + x + 2 = 156<\/li><li>3x + 3 = 156<\/li><li>3x = 156 &#8211; 3<\/li><li>3x = 153<\/li><li>x =  <strong><sup>153<\/sup>\u2044<sub>3<\/sub><\/strong> = 51, N\u00famero Menor<\/li><li>x +1 = 51 +1 = 52, el n\u00famero Intermedio<\/li><li>x + 2 = 51 + 2 = 53, el n\u00famero Mayor<\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"has-text-color has-background has-medium-font-size has-very-light-gray-color has-vivid-red-background-color\"><strong>Ejercicios:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_150318-scaled.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"467\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_150318-1024x467.jpg\" alt=\"\" class=\"wp-image-2193\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_150318-1024x467.jpg 1024w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_150318-300x137.jpg 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_150318-768x350.jpg 768w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_150318-1536x700.jpg 1536w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/11\/20191113_150318-2048x933.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<p>Saluditos<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Igualdad, expresi\u00f3n de que dos cantidades o expresiones algebraicas tienen el mismo Valor. Ecuaci\u00f3n, igualdad donde hay cantidades desconocidas llamadas inc\u00f3gnitas, quienes son representadas por las \u00faltimas letras del alfabeto: x, y, z, u, v, Ejemplo: 5x + 2 =17<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[49],"tags":[],"class_list":["post-2174","post","type-post","status-publish","format-standard","hentry","category-tercerparcialmate"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2174","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2174"}],"version-history":[{"count":14,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2174\/revisions"}],"predecessor-version":[{"id":2197,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2174\/revisions\/2197"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2174"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}