{"id":12957,"date":"2017-11-01T11:01:47","date_gmt":"2017-11-01T11:01:47","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12957"},"modified":"2022-01-09T00:08:38","modified_gmt":"2022-01-09T00:08:38","slug":"tres-inequacoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12957","title":{"rendered":"Tr\u00eas inequa\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_12957' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12957' class='GTTabs_curr'><a  id=\"12957_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12957' ><a  id=\"12957_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_12957'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera as seguintes inequa\u00e7\u00f5es:<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{6x &#8211; 2 &lt; 0}&amp;{}&amp;{ &#8211; 6x \\le &#8211; 2}&amp;{}&amp;{ &#8211; 3x + 2 &gt; 1}\\end{array}\\]<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Resolve cada uma das inequa\u00e7\u00f5es, apresentando o conjunto-solu\u00e7\u00e3o na forma de intervalo.<\/li>\n<li>Existem inequa\u00e7\u00f5es equivalentes entre as apresentadas?<br \/>\nSe sim, quais? Justifica a tua resposta.<\/li>\n<li>Os n\u00fameros \\(\\frac{1}{3}\\) e \\( &#8211; \\frac{1}{3}\\) s\u00e3o solu\u00e7\u00f5es comuns \u00e0s tr\u00eas inequa\u00e7\u00f5es? Justifica.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12957' onClick='GTTabs_show(1,12957)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12957'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>\\[\\begin{array}{*{20}{c}}{6x &#8211; 2 &lt; 0}&amp;{}&amp;{ &#8211; 6x \\le &#8211; 2}&amp;{}&amp;{ &#8211; 3x + 2 &gt; 1}\\end{array}\\]<\/p>\n<\/blockquote>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Resolvendo as inequa\u00e7\u00f5es, temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{6x &#8211; 2 &lt; 0}&amp; \\Leftrightarrow &amp;{6x &lt; 2}\\\\{}&amp; \\Leftrightarrow &amp;{x &lt; \\frac{1}{3}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\;\\frac{1}{3}} \\right[}\\end{array}\\]<br \/>\n\\[\\begin{array}{*{20}{l}}{ &#8211; 6x \\le &#8211; 2}&amp; \\Leftrightarrow &amp;{6x \\ge 2}\\\\{}&amp; \\Leftrightarrow &amp;{x \\ge \\frac{1}{3}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left[ {\\frac{1}{3},\\; + \\infty } \\right[}\\end{array}\\]<br \/>\n\\[\\begin{array}{*{20}{l}}{ &#8211; 3x + 2 &gt; 1}&amp; \\Leftrightarrow &amp;{ &#8211; 3x &gt; &#8211; 1}\\\\{}&amp; \\Leftrightarrow &amp;{x &lt; \\frac{1}{3}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\;\\frac{1}{3}} \\right[}\\end{array}\\]<br \/>\n\u00ad<\/li>\n<li>A primeira e terceira inequa\u00e7\u00f5es s\u00e3o equivalentes, pois possuem o mesmo conjunto-solu\u00e7\u00e3o.<br \/>\n\u00ad<\/li>\n<li>Nenhum desses valores (\\(\\frac{1}{3}\\) e \\( &#8211; \\frac{1}{3}\\)) \u00e9 solu\u00e7\u00e3o comum \u00e0s tr\u00eas inequa\u00e7\u00f5es, pois nenhum deles pertence simultaneamente aos respetivos conjuntos-solu\u00e7\u00e3o.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12957' onClick='GTTabs_show(0,12957)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera as seguintes inequa\u00e7\u00f5es: \\[\\begin{array}{*{20}{c}}{6x &#8211; 2 &lt; 0}&amp;{}&amp;{ &#8211; 6x \\le &#8211; 2}&amp;{}&amp;{ &#8211; 3x + 2 &gt; 1}\\end{array}\\] Resolve cada uma das inequa\u00e7\u00f5es, apresentando o conjunto-solu\u00e7\u00e3o na forma de&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19171,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[270,445],"series":[],"class_list":["post-12957","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-inequacao","tag-intervalo-de-numeros-reais"],"views":1611,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat62.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12957","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=12957"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12957\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19171"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12957"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12957"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12957"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12957"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}