{"id":24409,"date":"2023-02-07T15:44:57","date_gmt":"2023-02-07T15:44:57","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24409"},"modified":"2023-06-12T00:13:17","modified_gmt":"2023-06-11T23:13:17","slug":"resolve-as-equacoes-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24409","title":{"rendered":"Resolve as equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24409' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24409' class='GTTabs_curr'><a  id=\"24409_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24409' ><a  id=\"24409_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_24409'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve e classifica, em \\(\\mathbb{Q}\\), cada uma das seguintes equa\u00e7\u00f5es.<\/p>\n<ol>\n<li>\\(x + 4 = 3x &#8211; 5\\)<\/li>\n<li>\\(2\\left( {4 &#8211; 3x} \\right) = 7x &#8211; 5\\)<\/li>\n<li>\\(4\\left( {x &#8211; 1} \\right) &#8211; 5\\left( {x + 3} \\right) = &#8211; 19 &#8211; x\\)<\/li>\n<li>\\(6\\left( {\\frac{x}{3} + 1} \\right) &#8211; 2x + \\frac{1}{2} = 5\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24409' onClick='GTTabs_show(1,24409)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24409'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{x + 4 = 3x &#8211; 5}&amp; \\Leftrightarrow &amp;{x &#8211; 3x = &#8211; 4 &#8211; 5}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 2x = &#8211; 9}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{9}{2}}\\end{array}\\]<br \/>A equa\u00e7\u00e3o \u00e9 poss\u00edvel e determinada em \\(\\mathbb{Q}\\).<br \/>O conjunto-solu\u00e7\u00e3o \u00e9 \\(S = \\left\\{ {\\frac{9}{2}} \\right\\}\\).<br \/><br \/><\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{2\\left( {4 &#8211; 3x} \\right) = 7x &#8211; 5}&amp; \\Leftrightarrow &amp;{8 &#8211; 6x = 7x &#8211; 5}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 6x &#8211; 7x = &#8211; 8 &#8211; 5}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; 13x = &#8211; 13}\\\\{}&amp; \\Leftrightarrow &amp;{x = 1}\\end{array}\\]<br \/>A equa\u00e7\u00e3o \u00e9 poss\u00edvel e determinada em \\(\\mathbb{Q}\\).<br \/>O conjunto-solu\u00e7\u00e3o \u00e9 \\(S = \\left\\{ 1 \\right\\}\\).<br \/><br \/><\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{4\\left( {x &#8211; 1} \\right) &#8211; 5\\left( {x + 3} \\right) = &#8211; 19 &#8211; x}&amp; \\Leftrightarrow &amp;{4x &#8211; 4 &#8211; 5x &#8211; 15 = &#8211; 19 &#8211; x}\\\\{}&amp; \\Leftrightarrow &amp;{4x &#8211; 5x + x = 4 + 15 &#8211; 19}\\\\{}&amp; \\Leftrightarrow &amp;{0x = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x \\in \\mathbb{Q}}\\end{array}\\]<br \/>A equa\u00e7\u00e3o \u00e9 poss\u00edvel e indeterminada em \\(\\mathbb{Q}\\).<br \/>O conjunto-solu\u00e7\u00e3o \u00e9 \\(S = \\mathbb{Q}\\).<br \/><br \/><\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{6\\left( {\\frac{x}{3} + 1} \\right) &#8211; 2x + \\frac{1}{2} = 5}&amp; \\Leftrightarrow &amp;{2x + 6 &#8211; 2x + \\frac{1}{2} = 5}\\\\{}&amp; \\Leftrightarrow &amp;{0x = &#8211; 6 &#8211; \\frac{1}{2} + 5}\\\\{}&amp; \\Leftrightarrow &amp;{0x = &#8211; \\frac{3}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{x \\in \\emptyset }\\end{array}\\]<br \/>A equa\u00e7\u00e3o \u00e9 imposs\u00edvel em \\(\\mathbb{Q}\\).<br \/>O conjunto-solu\u00e7\u00e3o \u00e9 \\(S = \\left\\{ {} \\right\\}\\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24409' onClick='GTTabs_show(0,24409)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve e classifica, em \\(\\mathbb{Q}\\), cada uma das seguintes equa\u00e7\u00f5es. \\(x + 4 = 3x &#8211; 5\\) \\(2\\left( {4 &#8211; 3x} \\right) = 7x &#8211; 5\\) \\(4\\left( {x &#8211; 1} \\right)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14061,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,701],"series":[],"class_list":["post-24409","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-monomios-e-polinomios","tag-8-o-ano","tag-equacao-do-1-o-grau"],"views":197,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat06.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24409","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=24409"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24409\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14061"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24409"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}