{"id":11733,"date":"2014-02-02T01:23:56","date_gmt":"2014-02-02T01:23:56","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11733"},"modified":"2021-12-26T02:34:42","modified_gmt":"2021-12-26T02:34:42","slug":"sabendo-que-a-razao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11733","title":{"rendered":"Sabendo que a raz\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_11733' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11733' class='GTTabs_curr'><a  id=\"11733_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11733' ><a  id=\"11733_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_11733'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sabendo que a raz\u00e3o \\[\\frac{{x + 2}}{{x &#8211; 5}}\\] \u00e9 um valor maior do que $30$% de $x$, determine o valor de $x$.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11733' onClick='GTTabs_show(1,11733)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11733'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>\\[\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{x + 2}}{{x &#8211; 5}} &gt; \\frac{3}{{10}}x}&amp; \\Leftrightarrow &amp;{\\frac{{10x + 20 &#8211; 3{x^2} + 15x}}{{10\\left( {x &#8211; 5} \\right)}} &gt; 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\frac{{ &#8211; 3{x^2} + 25x + 20}}{{10\\left( {x &#8211; 5} \\right)}} &gt; 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{\\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{ &#8211; 3{x^2} + 25x + 20 &gt; 0} \\\\<br \/>\n{10\\left( {x &#8211; 5} \\right) &gt; 0}<br \/>\n\\end{array}} \\right.}&amp; \\vee &amp;{\\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{ &#8211; 3{x^2} + 25x + 20 &lt; 0} \\\\<br \/>\n{10\\left( {x &#8211; 5} \\right) &lt; 0}<br \/>\n\\end{array}} \\right.}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{\\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{x \\in \\left] {\\frac{{ &#8211; 25 + \\sqrt {865} }}{{ &#8211; 6}},\\frac{{ &#8211; 25 &#8211; \\sqrt {865} }}{{ &#8211; 6}}} \\right[} \\\\<br \/>\n{x &gt; 5}<br \/>\n\\end{array}} \\right.}&amp; \\vee &amp;{\\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{x \\in \\left] { &#8211; \\infty ,\\frac{{ &#8211; 25 + \\sqrt {865} }}{{ &#8211; 6}}} \\right[ \\cup \\left] {\\frac{{ &#8211; 25 &#8211; \\sqrt {865} }}{{ &#8211; 6}}, + \\infty } \\right[} \\\\<br \/>\n{x &lt; 5}<br \/>\n\\end{array}} \\right.}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{\\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{x \\in \\left] {\\frac{{25 &#8211; \\sqrt {865} }}{6},\\frac{{25 + \\sqrt {865} }}{6}} \\right[} \\\\<br \/>\n{x &gt; 5}<br \/>\n\\end{array}} \\right.}&amp; \\vee &amp;{\\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{x \\in \\left] { &#8211; \\infty ,\\frac{{25 &#8211; \\sqrt {865} }}{6}} \\right[ \\cup \\left] {\\frac{{25 + \\sqrt {865} }}{6}, + \\infty } \\right[} \\\\<br \/>\n{x &lt; 5}<br \/>\n\\end{array}} \\right.}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x \\in \\left] { &#8211; \\infty ,\\frac{{25 &#8211; \\sqrt {865} }}{6}} \\right[ \\cup \\left] {5,\\frac{{25 + \\sqrt {865} }}{6}} \\right[}<br \/>\n\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11733' onClick='GTTabs_show(0,11733)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabendo que a raz\u00e3o \\[\\frac{{x + 2}}{{x &#8211; 5}}\\] \u00e9 um valor maior do que $30$% de $x$, determine o valor de $x$. 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":[98,97,125],"tags":[422,126,270],"series":[],"class_list":["post-11733","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-racionais","tag-11-o-ano","tag-funcao-racional","tag-inequacao"],"views":2137,"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\/11733","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=11733"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11733\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11733"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11733"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11733"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}