{"id":12921,"date":"2017-10-31T18:21:38","date_gmt":"2017-10-31T18:21:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12921"},"modified":"2022-01-16T00:53:43","modified_gmt":"2022-01-16T00:53:43","slug":"determina-o-conjunto-solucao-de-cada-uma-das-condicoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12921","title":{"rendered":"Determina o conjunto-solu\u00e7\u00e3o de cada uma das condi\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_12921' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12921' class='GTTabs_curr'><a  id=\"12921_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12921' ><a  id=\"12921_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_12921'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina o conjunto-solu\u00e7\u00e3o de cada uma das condi\u00e7\u00f5es:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\({x &#8211; 1 \\le 7}\\)<\/li>\n<li>\\({\\left| x \\right| &gt; 3}\\)<\/li>\n<li>\\({1 &lt; \\frac{{x &#8211; 3}}{2} \\le 7}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12921' onClick='GTTabs_show(1,12921)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12921'>\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}}{x &#8211; 1 \\le 7}&amp; \\Leftrightarrow &amp;{x \\le 8}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\;8} \\right]}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{\\left| x \\right| &gt; 3}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x &lt; &#8211; 3}&amp; \\vee &amp;{x &gt; 3}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\; &#8211; 3} \\right[ \\cup \\left] {3,\\; + \\infty } \\right[}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{1 &lt; \\frac{{x &#8211; 3}}{2} \\le 7}&amp; \\Leftrightarrow &amp;{2 &lt; x &#8211; 3 \\le 14}\\\\{}&amp; \\Leftrightarrow &amp;{2 + 3 &lt; x &#8211; 3 + 3 \\le 14 + 3}\\\\{}&amp; \\Leftrightarrow &amp;{5 &lt; x \\le 17}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] {5,\\;17} \\right]}\\end{array}\\]<\/p>\n<p>\u00ad<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{1 &lt; \\frac{{x &#8211; 3}}{2} \\le 7}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{1 &lt; \\frac{{x &#8211; 3}}{2}}&amp; \\wedge &amp;{\\frac{{x &#8211; 3}}{2} \\le 7}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{2 &lt; x &#8211; 3}&amp; \\wedge &amp;{x &#8211; 3 \\le 14}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x &gt; 5}&amp; \\wedge &amp;{x \\le 17}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] {5,\\;17} \\right]}\\end{array}\\]<br \/>\n\u00ad<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{1 &lt; \\frac{{x &#8211; 3}}{2} \\le 7}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{c}}{1 &lt; \\frac{{x &#8211; 3}}{2}}\\\\{\\frac{{x &#8211; 3}}{2} \\le 7}\\end{array}} \\right.}\\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{c}}{2 &lt; x &#8211; 3}\\\\{x &#8211; 3 \\le 14}\\end{array}} \\right.}\\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{c}}{x &gt; 5}\\\\{x \\le 17}\\end{array}} \\right.}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] {5,\\;17} \\right]}\\end{array}\\]<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12921' onClick='GTTabs_show(0,12921)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina o conjunto-solu\u00e7\u00e3o de cada uma das condi\u00e7\u00f5es: \\({x &#8211; 1 \\le 7}\\) \\({\\left| x \\right| &gt; 3}\\) \\({1 &lt; \\frac{{x &#8211; 3}}{2} \\le 7}\\) Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20327,"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-12921","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":2732,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/9V1Pag036-17_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12921","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=12921"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12921\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20327"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12921"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12921"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12921"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}