{"id":7306,"date":"2012-01-08T17:42:30","date_gmt":"2012-01-08T17:42:30","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7306"},"modified":"2022-01-08T17:18:44","modified_gmt":"2022-01-08T17:18:44","slug":"sobre-um-numero-real","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7306","title":{"rendered":"Sobre um n\u00famero real"},"content":{"rendered":"<p><ul id='GTTabs_ul_7306' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7306' class='GTTabs_curr'><a  id=\"7306_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7306' ><a  id=\"7306_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_7306'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um n\u00famero $x$ verifica a condi\u00e7\u00e3o $\\frac{2}{3}&lt;x&lt;\\frac{3}{4}$.<\/p>\n<p>Enquadra os seguintes n\u00fameros:<\/p>\n<ol>\n<li>$x-1$<\/li>\n<li>$x+2$<\/li>\n<li>$3x$<\/li>\n<li>$-4x$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7306' onClick='GTTabs_show(1,7306)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7306'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Pela monotonia da adi\u00e7\u00e3o, adicionando $-1$ a ambos os membros da desigualdade, vem: $$\\begin{array}{*{35}{l}}<br \/>\n\\frac{2}{3}&lt;x&lt;\\frac{3}{4} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{2}{\\underset{(1)}{\\mathop{3}}\\,}-\\underset{(3)}{\\mathop{1}}\\,&lt;x-1&lt;\\frac{3}{\\underset{(1)}{\\mathop{4}}\\,}-\\underset{(4)}{\\mathop{1}}\\,\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -\\frac{1}{3}&lt;x-1&lt;-\\frac{1}{4}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\n\u00ad<\/li>\n<li>\u00a0Pela monotonia da adi\u00e7\u00e3o, adicionando $2$ a ambos os membros da desigualdade, vem: $$\\begin{array}{*{35}{l}}<br \/>\n\\frac{2}{3}&lt;x&lt;\\frac{3}{4} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{2}{\\underset{(1)}{\\mathop{3}}\\,}+\\underset{(3)}{\\mathop{2}}\\,&lt;x+2&lt;\\frac{3}{\\underset{(1)}{\\mathop{4}}\\,}+\\underset{(4)}{\\mathop{2}}\\,\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{8}{3}&lt;x+2&lt;\\frac{11}{4}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\n\u00ad<\/li>\n<li>Pela monotonia parcial da multiplica\u00e7\u00e3o, multiplicando\u00a0por $3$ ambos os membros da desigualdade, vem: $$\\begin{array}{*{35}{l}}<br \/>\n\\frac{2}{3}&lt;x&lt;\\frac{3}{4} &amp; \\Leftrightarrow\u00a0 &amp; 3\\times \\frac{2}{3}&lt;3\\times x&lt;3\\times \\frac{3}{4}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 2&lt;3x&lt;\\frac{9}{4}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\n\u00ad<\/li>\n<li>Pela monotonia parcial da multiplica\u00e7\u00e3o, multiplicando\u00a0por $-4$ ambos os membros da desigualdade, vem: $$\\begin{array}{*{35}{l}}<br \/>\n\\frac{2}{3}&lt;x&lt;\\frac{3}{4} &amp; \\Leftrightarrow\u00a0 &amp; -4\\times \\frac{2}{3}&gt;-4\\times x&gt;-4\\times \\frac{3}{4}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -\\frac{8}{3}&gt;-4x&gt;-3\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -3&lt;-4x&lt;-\\frac{8}{3}\u00a0 \\\\<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7306' onClick='GTTabs_show(0,7306)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um n\u00famero $x$ verifica a condi\u00e7\u00e3o $\\frac{2}{3}&lt;x&lt;\\frac{3}{4}$. Enquadra os seguintes n\u00fameros: $x-1$ $x+2$ $3x$ $-4x$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[426,270,266],"series":[],"class_list":["post-7306","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-9-o-ano","tag-inequacao","tag-numeros-reais"],"views":1750,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7306","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=7306"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7306\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14114"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7306"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}