{"id":12963,"date":"2017-11-01T11:37:25","date_gmt":"2017-11-01T11:37:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12963"},"modified":"2022-01-09T00:12:57","modified_gmt":"2022-01-09T00:12:57","slug":"sobre-uma-inequacao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12963","title":{"rendered":"Sobre uma inequa\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_12963' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12963' class='GTTabs_curr'><a  id=\"12963_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12963' ><a  id=\"12963_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_12963'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera a inequa\u00e7\u00e3o<\/p>\n<p>\\[x &#8211; \\frac{1}{3} &gt; \\frac{x}{2} + \\frac{1}{4}\\]<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>O n\u00famero 2 \u00e9 solu\u00e7\u00e3o?<\/li>\n<li>Quais s\u00e3o os n\u00fameros reais que satisfazem a inequa\u00e7\u00e3o?<\/li>\n<li>Existe algum n\u00famero negativo que seja solu\u00e7\u00e3o?<br \/>\nJustifica a tua solu\u00e7\u00e3o.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12963' onClick='GTTabs_show(1,12963)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12963'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>\\[x &#8211; \\frac{1}{3} &gt; \\frac{x}{2} + \\frac{1}{4}\\]<\/p>\n<\/blockquote>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Substituindo x por 2 na inequa\u00e7\u00e3o dada, temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{2 &#8211; \\frac{1}{3} &gt; \\frac{2}{2} + \\frac{1}{4}}&amp; \\Leftrightarrow &amp;{\\underbrace {\\frac{5}{3} &gt; \\frac{5}{4}}_{{\\rm{Proposi\u00e7\u00e3o verdadeira}}}}\\end{array}\\]<br \/>\nConclui-se que 2 \u00e9 solu\u00e7\u00e3o da inequa\u00e7\u00e3o, pois obteve-se uma proposi\u00e7\u00e3o verdadeira.<br \/>\n\u00ad<\/li>\n<li>Resolvendo a inequa\u00e7\u00e3o, vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{x &#8211; \\frac{1}{3} &gt; \\frac{x}{2} + \\frac{1}{4}}&amp; \\Leftrightarrow &amp;{12x &#8211; 4 &gt; 6x + 3}\\\\{}&amp; \\Leftrightarrow &amp;{6x &gt; 7}\\\\{}&amp; \\Leftrightarrow &amp;{x &gt; \\frac{7}{6}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] {\\frac{7}{6},\\; + \\infty } \\right[}\\end{array}\\]<br \/>\nOs n\u00fameros reais que\u00a0que satisfazem a inequa\u00e7\u00e3o s\u00e3o os maiores do que\u00a0\\({\\frac{7}{6}}\\).<br \/>\n\u00ad<\/li>\n<li>N\u00e3o, n\u00e3o existe qualquer n\u00famero negativo que seja solu\u00e7\u00e3o da inequa\u00e7\u00e3o, pois o seu conjunto-solu\u00e7\u00e3o n\u00e3o cont\u00e9m qualquer n\u00famero negativo<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12963' onClick='GTTabs_show(0,12963)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a inequa\u00e7\u00e3o \\[x &#8211; \\frac{1}{3} &gt; \\frac{x}{2} + \\frac{1}{4}\\] O n\u00famero 2 \u00e9 solu\u00e7\u00e3o? Quais s\u00e3o os n\u00fameros reais que satisfazem a inequa\u00e7\u00e3o? Existe algum n\u00famero negativo que seja solu\u00e7\u00e3o?&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14113,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[270],"series":[],"class_list":["post-12963","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-inequacao"],"views":1704,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat55.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12963"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12963\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14113"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12963"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12963"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12963"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}