{"id":12879,"date":"2017-10-30T02:28:30","date_gmt":"2017-10-30T02:28:30","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12879"},"modified":"2022-01-08T23:01:32","modified_gmt":"2022-01-08T23:01:32","slug":"qual-e-o-conjunto-solucao-de-cada-uma-das-seguintes-condicoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12879","title":{"rendered":"Qual \u00e9 o conjunto-solu\u00e7\u00e3o de cada uma das seguintes condi\u00e7\u00f5es?"},"content":{"rendered":"<p><ul id='GTTabs_ul_12879' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12879' class='GTTabs_curr'><a  id=\"12879_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12879' ><a  id=\"12879_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_12879'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Qual \u00e9 o conjunto-solu\u00e7\u00e3o de cada uma das seguintes condi\u00e7\u00f5es?<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\({\\begin{array}{*{20}{c}}{x \\ge &#8211; 3}&amp; \\vee &amp;{x \\ge 2}\\end{array}}\\)<\/li>\n<li>\\({ &#8211; 5 &lt; x \\le 7}\\)<\/li>\n<li>\\({\\begin{array}{*{20}{c}}{3y + 1 &lt; 7}&amp; \\vee &amp;{y &#8211; 8 &gt; 11}\\end{array}}\\)<\/li>\n<li>\\({\\begin{array}{*{20}{c}}{2x &#8211; 1 &gt; 5}&amp; \\wedge &amp;{4 &#8211; x &lt; 7}\\end{array}}\\)<\/li>\n<li>\\({\\begin{array}{*{20}{c}}{a &#8211; 4 &gt; \\frac{a}{2} &#8211; \\frac{1}{5}}&amp; \\vee &amp;{a + 1 &lt; 3a + 2}\\end{array}}\\)<\/li>\n<li>\\({\\begin{array}{*{20}{c}}{2\\left( {2 &#8211; x} \\right) &lt; x &#8211; 14}&amp; \\wedge &amp;{\\frac{x}{2} \\le 7 &#8211; \\frac{x}{5}}\\end{array}}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12879' onClick='GTTabs_show(1,12879)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12879'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{\\begin{array}{*{20}{c}}{x \\ge &#8211; 3}&amp; \\vee &amp;{x \\ge 2}\\end{array}}&amp; \\Leftrightarrow &amp;{x \\ge &#8211; 3}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left[ { &#8211; 3,\\; + \\infty } \\right[}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{ &#8211; 5 &lt; x \\le 7}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x &gt; &#8211; 5}&amp; \\wedge &amp;{x \\le 7}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; 5,\\;7} \\right]}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{\\begin{array}{*{20}{c}}{3y + 1 &lt; 7}&amp; \\vee &amp;{y &#8211; 8 &gt; 11}\\end{array}}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{3y &lt; 6}&amp; \\vee &amp;{y &gt; 19}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{y &lt; 2}&amp; \\vee &amp;{y &gt; 19}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\;2} \\right[ \\cup \\left] {19,\\; + \\infty } \\right[}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{\\begin{array}{*{20}{c}}{2x &#8211; 1 &gt; 5}&amp; \\wedge &amp;{4 &#8211; x &lt; 7}\\end{array}}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{2x &gt; 6}&amp; \\wedge &amp;{ &#8211; x &lt; 3}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x &gt; 3}&amp; \\wedge &amp;{x &gt; &#8211; 3}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{x &gt; 3}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] {3,\\; + \\infty } \\right[}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{\\begin{array}{*{20}{c}}{\\mathop a\\limits_{\\left( {10} \\right)} &#8211; \\mathop 4\\limits_{\\left( {10} \\right)} &gt; \\frac{a}{{\\mathop 2\\limits_{\\left( 5 \\right)} }} &#8211; \\frac{1}{{\\mathop 5\\limits_{\\left( 2 \\right)} }}}&amp; \\vee &amp;{a + 1 &lt; 3a + 2}\\end{array}}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{10a &#8211; 40 &gt; 5a &#8211; 2}&amp; \\vee &amp;{ &#8211; 2a &lt; 1}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{5a &gt; 38}&amp; \\vee &amp;{a &gt; &#8211; \\frac{1}{2}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{a &gt; \\frac{{38}}{5}}&amp; \\vee &amp;{a &gt; &#8211; \\frac{1}{2}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{a &gt; &#8211; \\frac{1}{2}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\frac{1}{2},\\; + \\infty } \\right[}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{\\begin{array}{*{20}{c}}{2\\left( {2 &#8211; x} \\right) &lt; x &#8211; 14}&amp; \\wedge &amp;{\\frac{x}{2} \\le 7 &#8211; \\frac{x}{5}}\\end{array}}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{4 &#8211; 2x &lt; x &#8211; 14}&amp; \\wedge &amp;{5x \\le 70 &#8211; 2x}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{ &#8211; 3x &lt; &#8211; 18}&amp; \\wedge &amp;{7x \\le 70}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x &gt; 6}&amp; \\wedge &amp;{x \\le 10}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] {6,\\;10} \\right]}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12879' onClick='GTTabs_show(0,12879)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Qual \u00e9 o conjunto-solu\u00e7\u00e3o de cada uma das seguintes condi\u00e7\u00f5es? \\({\\begin{array}{*{20}{c}}{x \\ge &#8211; 3}&amp; \\vee &amp;{x \\ge 2}\\end{array}}\\) \\({ &#8211; 5 &lt; x \\le 7}\\) \\({\\begin{array}{*{20}{c}}{3y + 1 &lt; 7}&amp; \\vee&#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":[446,447,270,445],"series":[],"class_list":["post-12879","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-conjuncao-de-inequacoes","tag-disjuncao-de-inequacoes","tag-inequacao","tag-intervalo-de-numeros-reais"],"views":2649,"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\/12879","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=12879"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12879\/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=12879"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12879"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12879"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12879"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}