{"id":12961,"date":"2017-11-01T11:23:15","date_gmt":"2017-11-01T11:23:15","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12961"},"modified":"2022-01-09T00:09:51","modified_gmt":"2022-01-09T00:09:51","slug":"determina-a-soma-dos-numeros-inteiros-maiores-do-que-6-que-satisfazem-a-seguinte-inequacao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12961","title":{"rendered":"Determina a soma dos n\u00fameros inteiros maiores do que -6 que satisfazem a seguinte inequa\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_12961' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12961' class='GTTabs_curr'><a  id=\"12961_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12961' ><a  id=\"12961_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_12961'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina a soma dos n\u00fameros inteiros maiores do que -6 que satisfazem a seguinte inequa\u00e7\u00e3o:<\/p>\n<p>\\[2 &#8211; \\frac{{x &#8211; 2}}{4} &gt; 3 + \\frac{{x &#8211; 3}}{3}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12961' onClick='GTTabs_show(1,12961)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12961'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\mathop 2\\limits_{\\left( {12} \\right)} &#8211; \\frac{{x &#8211; 2}}{{\\mathop 4\\limits_{\\left( 3 \\right)} }} &gt; \\mathop 3\\limits_{\\left( {12} \\right)} + \\frac{{x &#8211; 3}}{{\\mathop 3\\limits_{\\left( 4 \\right)} }}}&amp; \\Leftrightarrow &amp;{24 &#8211; 3x + 6 &gt; 36 + 4x &#8211; 12}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 7x &gt; &#8211; 6}\\\\{}&amp; \\Leftrightarrow &amp;{x &lt; \\frac{6}{7}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\;\\frac{6}{7}} \\right[}\\end{array}\\]<\/p>\n<p>Portanto,\u00a0a soma dos n\u00fameros inteiros maiores do que -6 que satisfazem a inequa\u00e7\u00e3o \u00e9:<\/p>\n<p>\\[ &#8211; 5 + \\left( { &#8211; 4} \\right) + \\left( { &#8211; 3} \\right) + \\left( { &#8211; 2} \\right) + \\left( { &#8211; 1} \\right) + 0 = &#8211; 15\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12961' onClick='GTTabs_show(0,12961)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina a soma dos n\u00fameros inteiros maiores do que -6 que satisfazem a seguinte inequa\u00e7\u00e3o: \\[2 &#8211; \\frac{{x &#8211; 2}}{4} &gt; 3 + \\frac{{x &#8211; 3}}{3}\\] Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14083,"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-12961","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":2698,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12961","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=12961"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12961\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14083"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12961"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12961"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12961"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12961"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}