{"id":12918,"date":"2017-10-31T17:34:25","date_gmt":"2017-10-31T17:34:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12918"},"modified":"2022-01-16T00:48:48","modified_gmt":"2022-01-16T00:48:48","slug":"resolve-as-seguintes-inequacoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12918","title":{"rendered":"Resolve as seguintes inequa\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_12918' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12918' class='GTTabs_curr'><a  id=\"12918_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12918' ><a  id=\"12918_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_12918'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve as seguintes inequa\u00e7\u00f5es, representando o conjunto-solu\u00e7\u00e3o sob a forma de intervalo de n\u00fameros reais.<\/p>\n<p>h)\u00a0\\(2x &#8211; \\frac{3}{2} &lt; 4x + \\frac{{2x &#8211; 1}}{2}\\)<\/p>\n<p>\u00a0i)\u00a0\\(\\frac{{5x + 1}}{2} &#8211; \\frac{{x &#8211; 7}}{3} \\ge x\\)<\/p>\n<p>j)\u00a0\\(\\frac{3}{4}\\left( {x + 1} \\right) \\le 7 &#8211; \\frac{2}{3}\\left( {1 &#8211; x} \\right)\\)<\/p>\n<p>k)\u00a0\\(\\frac{{3 &#8211; x}}{5} + 0,1\\left( {2x + 1} \\right) \\ge 0\\)<\/p>\n<p>l)\u00a0\\(\\frac{{0,2x &#8211; 1}}{3} \\ge \\frac{{0,8 &#8211; x}}{2}\\)<\/p>\n<p>m)\u00a0\\( &#8211; x &#8211; \\frac{{2\\left( {8x &#8211; 3} \\right)}}{{21}} &gt; \\frac{{3x}}{7} &#8211; \\frac{{5 &#8211; 3x}}{7}\\)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12918' onClick='GTTabs_show(1,12918)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12918'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>h)<br \/>\n\\[\\begin{array}{*{20}{l}}{\\mathop {2x}\\limits_{\\left( 2 \\right)} &#8211; \\frac{3}{{\\mathop 2\\limits_{\\left( 1 \\right)} }} &lt; \\mathop {4x}\\limits_{\\left( 2 \\right)} + \\frac{{2x &#8211; 1}}{{\\mathop 2\\limits_{\\left( 1 \\right)} }}}&amp; \\Leftrightarrow &amp;{4x &#8211; 3 &lt; 8x + 2x &#8211; 1}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 6x &lt; 2}\\\\{}&amp; \\Leftrightarrow &amp;{x &gt; &#8211; \\frac{1}{3}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\frac{1}{3},\\; + \\infty } \\right[}\\end{array}\\]<\/p>\n<p>\u00a0i)<br \/>\n\\[\\begin{array}{*{20}{l}}{\\frac{{5x + 1}}{{\\mathop 2\\limits_{\\left( 3 \\right)} }} &#8211; \\frac{{x &#8211; 7}}{{\\mathop 3\\limits_{\\left( 2 \\right)} }} \\ge \\mathop x\\limits_{\\left( 6 \\right)} }&amp; \\Leftrightarrow &amp;{15x + 3 &#8211; 2x + 14 \\ge 6x}\\\\{}&amp; \\Leftrightarrow &amp;{7x \\ge &#8211; 17}\\\\{}&amp; \\Leftrightarrow &amp;{x \\ge &#8211; \\frac{{17}}{7}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left[ { &#8211; \\frac{{17}}{7},\\; + \\infty } \\right[}\\end{array}\\]<\/p>\n<p>j)<br \/>\n\\[\\begin{array}{*{20}{l}}{\\frac{3}{{\\mathop 4\\limits_{\\left( 3 \\right)} }}\\left( {x + 1} \\right) \\le \\mathop 7\\limits_{\\left( {12} \\right)} &#8211; \\frac{2}{{\\mathop 3\\limits_{\\left( 4 \\right)} }}\\left( {1 &#8211; x} \\right)}&amp; \\Leftrightarrow &amp;{9\\left( {x + 1} \\right) \\le 84 &#8211; 8\\left( {1 &#8211; x} \\right)}\\\\{}&amp; \\Leftrightarrow &amp;{9x + 9 \\le 84 &#8211; 8 + 8x}\\\\{}&amp; \\Leftrightarrow &amp;{x \\le 67}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\;67} \\right]}\\end{array}\\]<\/p>\n<p>k)<br \/>\n\\[\\begin{array}{*{20}{l}}{\\frac{{3 &#8211; x}}{{\\mathop 5\\limits_{\\left( 2 \\right)} }} + \\mathop {0,1}\\limits_{\\left( {10} \\right)} \\left( {2x + 1} \\right) \\ge \\mathop 0\\limits_{\\left( {10} \\right)} }&amp; \\Leftrightarrow &amp;{6 &#8211; 2x + 1 \\times \\left( {2x + 1} \\right) \\ge 0}\\\\{}&amp; \\Leftrightarrow &amp;{0x \\ge &#8211; 7}\\\\{}&amp; \\Leftrightarrow &amp;{x \\in \\mathbb{R}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\; + \\infty } \\right]}\\end{array}\\]<\/p>\n<p>l)<br \/>\n\\[\\begin{array}{*{20}{l}}{\\frac{{0,2x &#8211; 1}}{{\\mathop 3\\limits_{\\left( 2 \\right)} }} \\ge \\frac{{0,8 &#8211; x}}{{\\mathop 2\\limits_{\\left( 3 \\right)} }}}&amp; \\Leftrightarrow &amp;{0,4x &#8211; 2 \\ge 2,4 &#8211; 3x}\\\\{}&amp; \\Leftrightarrow &amp;{4x &#8211; 20 \\ge 24 &#8211; 30x}\\\\{}&amp; \\Leftrightarrow &amp;{34x \\ge 44}\\\\{}&amp; \\Leftrightarrow &amp;{x \\ge \\frac{{22}}{{17}}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left[ {\\frac{{22}}{{17}},\\; + \\infty } \\right[}\\end{array}\\]<\/p>\n<p>m)<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\mathop { &#8211; x}\\limits_{\\left( {21} \\right)} &#8211; \\frac{{2\\left( {8x &#8211; 3} \\right)}}{{\\mathop {21}\\limits_{\\left( 1 \\right)} }} \\ge \\frac{{3x}}{{\\mathop 7\\limits_{\\left( 3 \\right)} }} &#8211; \\frac{{5 &#8211; 3x}}{{\\mathop 7\\limits_{\\left( 3 \\right)} }}}&amp; \\Leftrightarrow &amp;{ &#8211; 21x &#8211; 16x + 6 \\ge 9x &#8211; 15 + 9x}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 55x \\ge &#8211; 21}\\\\{}&amp; \\Leftrightarrow &amp;{x \\le \\frac{{21}}{{55}}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left] { &#8211; \\infty ,\\;\\frac{{21}}{{55}}} \\right]}\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12918' onClick='GTTabs_show(0,12918)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as seguintes inequa\u00e7\u00f5es, representando o conjunto-solu\u00e7\u00e3o sob a forma de intervalo de n\u00fameros reais. h)\u00a0\\(2x &#8211; \\frac{3}{2} &lt; 4x + \\frac{{2x &#8211; 1}}{2}\\) \u00a0i)\u00a0\\(\\frac{{5x + 1}}{2} &#8211; \\frac{{x &#8211; 7}}{3}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20326,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[270,449],"series":[],"class_list":["post-12918","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"],"views":2298,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/9V1Pag036-16_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12918","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=12918"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12918\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20326"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12918"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12918"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12918"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}