{"id":12846,"date":"2017-10-29T18:22:46","date_gmt":"2017-10-29T18:22:46","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12846"},"modified":"2022-01-08T22:48:42","modified_gmt":"2022-01-08T22:48:42","slug":"resolve-as-inequacoes-seguintes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12846","title":{"rendered":"Resolve as inequa\u00e7\u00f5es seguintes"},"content":{"rendered":"<p><ul id='GTTabs_ul_12846' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12846' class='GTTabs_curr'><a  id=\"12846_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12846' ><a  id=\"12846_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_12846'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve as inequa\u00e7\u00f5es seguintes:<\/p>\n<p>i)\u00a0\\(4x &#8211; 1 &lt; 3x + \\frac{1}{2}\\)<\/p>\n<p>k)\u00a0\\(5\\left( {1 + 3x} \\right) + \\frac{1}{2} \\ge 5x\\)<\/p>\n<p>l)\u00a0\\(\\frac{1}{3} + \\frac{1}{2}\\left( {x &#8211; 1} \\right) &lt; 2x + 1\\)<\/p>\n<p>m)\u00a0\\(\\frac{{y + 3}}{6} \\le 2 &#8211; \\frac{{4 &#8211; 3y}}{2}\\)<\/p>\n<p>n)\u00a0\\(\\frac{{7x &#8211; 3}}{4} &#8211; \\frac{{9x &#8211; 4}}{8} &gt; 0\\)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12846' onClick='GTTabs_show(1,12846)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12846'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>i) \\[\\begin{array}{*{20}{l}}{\\mathop {4x}\\limits_{\\left( 2 \\right)} &#8211; \\mathop 1\\limits_{\\left( 2 \\right)} &lt; \\mathop {3x}\\limits_{\\left( 2 \\right)} + \\frac{1}{{\\mathop 2\\limits_{\\left( 1 \\right)} }}}&amp; \\Leftrightarrow &amp;{8x &#8211; 2 &lt; 6x + 1}\\\\{}&amp; \\Leftrightarrow &amp;{2x &lt; 3}\\\\{}&amp; \\Leftrightarrow &amp;{x &lt; \\frac{3}{2}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\;\\frac{3}{2}} \\right[}\\end{array}\\]<\/p>\n<p>k) \\[\\begin{array}{*{20}{l}}{5\\left( {1 + 3x} \\right) + \\frac{1}{2} \\ge 5x}&amp; \\Leftrightarrow &amp;{5 + 15x + \\frac{1}{2} \\ge 5x}\\\\{}&amp; \\Leftrightarrow &amp;{10x \\ge &#8211; \\frac{{11}}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{x \\ge &#8211; \\frac{{11}}{{20}}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left[ { &#8211; \\frac{{11}}{{20}},\\; + \\infty } \\right[}\\end{array}\\]<\/p>\n<p>l) \\[\\begin{array}{*{20}{l}}{\\frac{1}{3} + \\frac{1}{2}\\left( {x &#8211; 1} \\right) &lt; 2x + 1}&amp; \\Leftrightarrow &amp;{\\frac{1}{{\\mathop 3\\limits_{\\left( 2 \\right)} }} + \\frac{x}{{\\mathop 2\\limits_{\\left( 3 \\right)} }} &#8211; \\frac{1}{{\\mathop 2\\limits_{\\left( 3 \\right)} }} &lt; \\mathop {2x}\\limits_{\\left( 6 \\right)} + \\mathop 1\\limits_{\\left( 6 \\right)} }\\\\{}&amp; \\Leftrightarrow &amp;{2 + 3x &#8211; 3 &lt; 12x + 6}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 9x &lt; 7}\\\\{}&amp; \\Leftrightarrow &amp;{x &gt; &#8211; \\frac{7}{9}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\frac{7}{9},\\; + \\infty } \\right[}\\end{array}\\]<\/p>\n<p>m) \\[\\begin{array}{*{20}{l}}{\\frac{{y + 3}}{{\\mathop 6\\limits_{\\left( 1 \\right)} }} \\le \\mathop 2\\limits_{\\left( 6 \\right)} &#8211; \\frac{{4 &#8211; 3y}}{{\\mathop 2\\limits_{\\left( 3 \\right)} }}}&amp; \\Leftrightarrow &amp;{y + 3 \\le 12 &#8211; 12 + 9y}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 8y \\le &#8211; 3}\\\\{}&amp; \\Leftrightarrow &amp;{y \\ge \\frac{3}{8}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left[ {\\frac{3}{8},\\; + \\infty } \\right[}\\end{array}\\]<\/p>\n<p>n) \\[\\begin{array}{*{20}{l}}{\\frac{{7x &#8211; 3}}{{\\mathop 4\\limits_{\\left( 2 \\right)} }} &#8211; \\frac{{9x &#8211; 4}}{{\\mathop 8\\limits_{\\left( 1 \\right)} }} &gt; \\mathop 0\\limits_{\\left( 8 \\right)} }&amp; \\Leftrightarrow &amp;{14x &#8211; 6 &#8211; 9x + 4 &gt; 0}\\\\{}&amp; \\Leftrightarrow &amp;{5x &gt; 2}\\\\{}&amp; \\Leftrightarrow &amp;{x &gt; \\frac{2}{5}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] {\\frac{2}{5},\\; + \\infty } \\right[}\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12846' onClick='GTTabs_show(0,12846)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as inequa\u00e7\u00f5es seguintes: i)\u00a0\\(4x &#8211; 1 &lt; 3x + \\frac{1}{2}\\) k)\u00a0\\(5\\left( {1 + 3x} \\right) + \\frac{1}{2} \\ge 5x\\) l)\u00a0\\(\\frac{1}{3} + \\frac{1}{2}\\left( {x &#8211; 1} \\right) &lt; 2x + 1\\)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19172,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[97,258],"tags":[270],"series":[],"class_list":["post-12846","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-aplicando","category-os-numeros-reais","tag-inequacao"],"views":1179,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat63.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12846","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=12846"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12846\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19172"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12846"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12846"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12846"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}