{"id":7309,"date":"2012-01-08T18:57:51","date_gmt":"2012-01-08T18:57:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7309"},"modified":"2022-01-08T17:25:11","modified_gmt":"2022-01-08T17:25:11","slug":"resolve-as-inequacoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7309","title":{"rendered":"Resolve as inequa\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_7309' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7309' class='GTTabs_curr'><a  id=\"7309_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7309' ><a  id=\"7309_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_7309'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve as inequa\u00e7\u00f5es:<\/p>\n<ol>\n<li>$-2x-3&gt;3x-13$<\/li>\n<li>$3(x+2)&lt;5(1+x)$<\/li>\n<li>$5(x+4)&gt;2x$<\/li>\n<li>$12x-(x-1)\\ge 7x$<\/li>\n<li>$5(1+3x)+\\frac{1}{2}&gt;5x$<\/li>\n<li>$\\frac{1}{3}+\\frac{1}{2}(x-1)&gt;2x+1$<\/li>\n<li>$\\frac{y+3}{6}\\le 2-\\frac{4-3y}{2}$<\/li>\n<li>$\\frac{7x-3}{4}-\\frac{9x-4}{8}&gt;0$<\/li>\n<li>${{(3+x)}^{2}}&gt;{{x}^{2}}-1+7x$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7309' onClick='GTTabs_show(1,7309)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7309'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n-2x-3&gt;3x-13 &amp; \\Leftrightarrow\u00a0 &amp; -2x-3x&gt;-13+3\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -5x&gt;-10\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{-5x}{-5}&lt;\\frac{-10}{-5}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x&lt;2\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9: \\[S=\\left] -\\infty ,2 \\right[\\]<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n3(x+2)&lt;5(1+x) &amp; \\Leftrightarrow\u00a0 &amp; 3x+6&lt;5+5x\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -2x&lt;-1\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{-2x}{-2}&gt;\\frac{-1}{-2}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x&gt;\\frac{1}{2}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9:\\[S=\\left] \\frac{1}{2},+\\infty\u00a0 \\right[\\]<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n5(x+4)&gt;2x &amp; \\Leftrightarrow\u00a0 &amp; 5x+20&gt;2x\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 3x&gt;-20\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{3x}{3}&gt;\\frac{-20}{3}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x&gt;-\\frac{20}{3}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9:\\[S=\\left] -\\frac{20}{3},+\\infty\u00a0 \\right[\\]<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n12x-(x-1)\\ge 7x &amp; \\Leftrightarrow\u00a0 &amp; 12x-x+1\\ge 7x\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 4x\\ge -1\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{4x}{4}\\ge \\frac{-1}{4}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x\\ge -\\frac{1}{4}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9:\\[S=\\left[ -\\frac{1}{4},+\\infty\u00a0 \\right[\\]<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n5(1+3x)+\\frac{1}{2}&gt;5x &amp; \\Leftrightarrow\u00a0 &amp; \\underset{(2)}{\\mathop{5}}\\,+\\underset{(2)}{\\mathop{15x}}\\,+\\frac{1}{\\underset{(1)}{\\mathop{2}}\\,}&gt;\\underset{(2)}{\\mathop{5x}}\\,\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 10+30x+1&gt;10x\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 20x&gt;-11\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x&gt;-\\frac{11}{20}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9:\\[S=\\left] -\\frac{11}{20},+\\infty\u00a0 \\right[\\]<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n\\frac{1}{3}+\\frac{1}{2}(x-1)&gt;2x+1 &amp; \\Leftrightarrow\u00a0 &amp; \\underset{(2)}{\\mathop{\\frac{1}{3}}}\\,+\\underset{(3)}{\\mathop{\\frac{x}{2}}}\\,-\\underset{(3)}{\\mathop{\\frac{1}{2}}}\\,&gt;\\underset{(6)}{\\mathop{2x}}\\,+\\underset{(6)}{\\mathop{1}}\\,\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 2+3x-3&gt;12x+6\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -9x&gt;7\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x&lt;-\\frac{7}{9}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9:\\[S=\\left] -\\infty ,-\\frac{7}{9} \\right[\\]<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n\\frac{y+3}{\\underset{(1)}{\\mathop{6}}\\,}\\le \\underset{(6)}{\\mathop{2}}\\,-\\frac{4-3y}{\\underset{(3)}{\\mathop{2}}\\,} &amp; \\Leftrightarrow\u00a0 &amp; y+3\\le 12-12+9y\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -8y\\le -3\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{-8y}{-8}\\ge \\frac{-3}{-8}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; y\\ge \\frac{3}{8}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9:\\[S=\\left[ \\frac{3}{8},+\\infty\u00a0 \\right[\\]<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n\\frac{7x-3}{\\underset{(2)}{\\mathop{4}}\\,}-\\frac{9x-4}{\\underset{(1)}{\\mathop{8}}\\,}&gt;\\underset{(8)}{\\mathop{0}}\\, &amp; \\Leftrightarrow\u00a0 &amp; 14x-6-9x+4&gt;0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 5x&gt;2\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x&gt;\\frac{2}{5}\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9:\\[S=\\left] \\frac{2}{5},+\\infty\u00a0 \\right[\\]<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\n{{(3+x)}^{2}}&gt;{{x}^{2}}-1+7x &amp; \\Leftrightarrow\u00a0 &amp; 9+6x+{{x}^{2}}&gt;{{x}^{2}}-1+7x\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -x&gt;-10\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x&lt;10\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nO conjunto solu\u00e7\u00e3o \u00e9:\\[S=\\left] -\\infty ,10 \\right[\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7309' onClick='GTTabs_show(0,7309)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as inequa\u00e7\u00f5es: $-2x-3&gt;3x-13$ $3(x+2)&lt;5(1+x)$ $5(x+4)&gt;2x$ $12x-(x-1)\\ge 7x$ $5(1+3x)+\\frac{1}{2}&gt;5x$ $\\frac{1}{3}+\\frac{1}{2}(x-1)&gt;2x+1$ $\\frac{y+3}{6}\\le 2-\\frac{4-3y}{2}$ $\\frac{7x-3}{4}-\\frac{9x-4}{8}&gt;0$ ${{(3+x)}^{2}}&gt;{{x}^{2}}-1+7x$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14113,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[426,270,271],"series":[],"class_list":["post-7309","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-os-numeros-reais-2"],"views":1916,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat55.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7309","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=7309"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7309\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14113"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7309"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7309"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7309"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}