{"id":17552,"date":"2020-08-21T17:12:40","date_gmt":"2020-08-21T20:12:40","guid":{"rendered":"https:\/\/beduka.com\/blog\/?p=17552"},"modified":"2020-08-21T17:39:25","modified_gmt":"2020-08-21T20:39:25","slug":"exercicios-inequacao","status":"publish","type":"post","link":"https:\/\/beduka.com\/blog\/exercicios\/matematica-exercicios\/exercicios-inequacao\/","title":{"rendered":"Exerc\u00edcios de inequa\u00e7\u00e3o do 1\u00b0 grau com Gabarito"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote\"><p> Uma inequa\u00e7\u00e3o do primeiro grau \u00e9 respons\u00e1vel por expressar uma desigualdade. Ao contr\u00e1rio da equa\u00e7\u00e3o, ela n\u00e3o iguala uma opera\u00e7\u00e3o a zero, ela a coloca como \u201cmaior que\u201d, \u201cmenor que\u201d, \u201cMaior ou igual a\u201d ou \u201cmenor ou igual a\u201d. Leia o nosso resumo e coloque em pr\u00e1tica seu conhecimento com exerc\u00edcios de Inequa\u00e7\u00e3o do 1\u00b0 grau. <\/p><\/blockquote>\n\n\n\n<p> Quando voc\u00ea terminar os exerc\u00edcios de <strong>Inequa\u00e7\u00e3o do 1\u00b0 grau<\/strong>, fa\u00e7a nosso <a href=\"https:\/\/beduka.com\/simulado-enem\/#\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Simulado Enem<\/a>. Coloque em pr\u00e1tica todo o seu estudo, escolhendo as mat\u00e9rias que deseja treinar. <\/p>\n\n\n\n<p>Apontamos que algo \u00e9 do primeiro ou do segundo grau a partir do expoente que eleva a vari\u00e1vel (geralmente representada por X). Ent\u00e3o:<\/p>\n\n\n\n<ul><li>X\u00b2 + 3X + 9 = 0, \u00e9 uma equa\u00e7\u00e3o do segundo grau pois X est\u00e1 elevado ao quadrado.<\/li><li>X + 9 = 0, \u00e9 uma equa\u00e7\u00e3o do primeiro grau pois X est\u00e1 elevado a um (X = X\u00b9)<\/li><\/ul>\n\n\n\n<p>No caso das inequa\u00e7\u00f5es, a mesma regra se aplica. Neste post aprenderemos e faremos exerc\u00edcios de inequa\u00e7\u00e3o do 1\u00b0 grau, ou seja, inequa\u00e7\u00f5es que n\u00e3o envolvem expoentes maiores do que 1.<\/p>\n\n\n\n<ul><li>Relembre o que \u00e9 a <a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/equacao-do-primeiro-grau\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Equa\u00e7\u00e3o do Primeiro Grau<\/a>.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">A Inequa\u00e7\u00e3o do 1\u00b0 grau<\/h2>\n\n\n\n<p>Inequa\u00e7\u00e3o do 1\u00b0 grau \u00e9 uma desigualdade que objetiva encontrar valores para a vari\u00e1vel (representada por alguma letra) que satisfa\u00e7am a compara\u00e7\u00e3o feita. Essa compara\u00e7\u00e3o pode ser das seguintes formas:<\/p>\n\n\n\n<ul><li>ax + b &gt; 0, ou seja,<strong> a opera\u00e7\u00e3o (ax + b) d\u00e1 um resultado maior (&gt;) do que zero;<\/strong><\/li><li>ax + b<strong> <\/strong>\u2265 0, ou seja, <strong>a opera\u00e7\u00e3o (ax + b) d\u00e1 um resultado maior (&gt;) ou igual (=) a zero;<\/strong><\/li><li>ax + b &lt; 0, ou seja,<strong> <\/strong><strong>a opera\u00e7\u00e3o (ax + b) d\u00e1 um resultado menor (&lt;) do que zero;<\/strong><\/li><li>ax + b \u2264 0, ou seja, <strong>a opera\u00e7\u00e3o (ax + b) d\u00e1 um resultado menor (&lt;) ou igual (=) a zero;<\/strong><\/li><\/ul>\n\n\n\n<p>Lembrando que isso vale se considerarmos <strong>a <\/strong>e <strong>b <\/strong>pertencentes ao conjunto dos n\u00fameros reais <strong>[R] <\/strong>e sendo <strong>a<\/strong> um n\u00famero diferente de 0 <strong>(a, b \u2208 R e a \u2260 0.)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/08\/inequa\u00e7\u00e3o-do-1\u00b0-grau-dica.jpg\" alt=\"Dica de Inequa\u00e7\u00e3o do 1\u00b0 grau\" class=\"wp-image-17554\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/08\/inequa\u00e7\u00e3o-do-1\u00b0-grau-dica.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/08\/inequa\u00e7\u00e3o-do-1\u00b0-grau-dica-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/08\/inequa\u00e7\u00e3o-do-1\u00b0-grau-dica-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Como resolver uma inequa\u00e7\u00e3o do 1\u00b0 grau?<\/h2>\n\n\n\n<p>Para resolver uma inequa\u00e7\u00e3o, precisamos encontrar um <strong>conjunto solu\u00e7\u00e3o. <\/strong>Por mais que o nome assuste, n\u00e3o \u00e9 nenhum bicho de sete cabe\u00e7as.<strong> O conjunto solu\u00e7\u00e3o s\u00e3o os valores poss\u00edveis para que a vari\u00e1vel assuma e resulte naquela senten\u00e7a que foi estabelecida na Inequa\u00e7\u00e3o.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-1 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/08\/inequa\u00e7\u00e3o-do-1\u00b0-grau-exemplo-1.jpg\" alt=\"Como resolver uma inequa\u00e7\u00e3o do 1\u00b0 grau\" data-id=\"17556\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=17556\" class=\"wp-image-17556\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/08\/inequa\u00e7\u00e3o-do-1\u00b0-grau-exemplo-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/08\/inequa\u00e7\u00e3o-do-1\u00b0-grau-exemplo-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/08\/inequa\u00e7\u00e3o-do-1\u00b0-grau-exemplo-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Exerc\u00edcios de inequa\u00e7\u00e3o do Primeiro Grau<\/h2>\n\n\n\n<p>No in\u00edcio at\u00e9 assusta, mas agora sei que com esse resumo tudo ficou mais claro para voc\u00ea. Que tal testar seu conhecimento com <strong>exerc\u00edcios de Inequa\u00e7\u00e3o do 1\u00b0 grau.<\/strong>&nbsp;<\/p>\n\n\n\n<p><strong>Parab\u00e9ns<\/strong> por ter lido at\u00e9 aqui!!!&nbsp;<\/p>\n\n\n\n<p>Baixe <strong>gratuitamente<\/strong> o <a href=\"https:\/\/beduka.com\/blog\/dicas\/enem-dicas\/plano-de-estudos-gratuito\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Plano de Estudos<\/a> do <strong>Beduka<\/strong> e tenha uma prepara\u00e7\u00e3o<strong> perfeita <\/strong>para o <strong>ENEM<\/strong>.<\/p>\n\n\n\n<p><strong>Quest\u00e3o 1 &#8211; <a href=\"http:\/\/www.unirio.br\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(Unirio \u2013 RJ)<\/a><\/strong> A diferen\u00e7a entre o comprimento x e a largura y de um ret\u00e2ngulo \u00e9 de 2 cm. Se a sua \u00e1rea \u00e9 menor ou igual a 24 cm\u00b2, ent\u00e3o, o valor de x, em cm, ser\u00e1:<\/p>\n\n\n\n<p><strong>a) <\/strong>0 &lt; x &lt; 6<\/p>\n\n\n\n<p><strong>b)<\/strong> 0 &lt; x \u2264 4&nbsp;<\/p>\n\n\n\n<p><strong>c) <\/strong>2 &lt; x \u2264 6<\/p>\n\n\n\n<p><strong>d) <\/strong>2 &lt; x &lt; 6<\/p>\n\n\n\n<p><strong>e)<\/strong> 2 &lt; x \u2264 4<\/p>\n\n\n\n<p><strong>Quest\u00e3o 2 &#8211; <a href=\"https:\/\/www.uva.br\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(UVA 2016)<\/a> <\/strong>Se x &lt; 6 e 6 &lt; y , pode-se dizer que:&nbsp;<\/p>\n\n\n\n<p><strong>a) <\/strong>x = y<\/p>\n\n\n\n<p><strong>b) <\/strong>x &gt; y4<\/p>\n\n\n\n<p><strong>c) <\/strong>x &lt; y<\/p>\n\n\n\n<p><strong>d) <\/strong>x = 6<\/p>\n\n\n\n<p><strong>Quest\u00e3o 3 &#8211;<\/strong> <strong><a href=\"https:\/\/exame3.ifal.edu.br\/exames\/listarExamesAnteriores\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(IFAL 2015)<\/a><\/strong> Para pintar sua casa, Marcos encontra dois pintores: Ant\u00f4nio, que cobra um valor contratual de R$ 100,00 e mais R$ 10,00 por m2 de \u00e1rea pintada, e Benedito, que cobra R$ 200,00 no contrato e mais R$ 6,00 por m2 de pintura. Acima de quantos m2 de \u00e1rea pintada \u00e9 mais econ\u00f4mico contratar Benedito?<\/p>\n\n\n\n<p><strong>a) <\/strong>5<\/p>\n\n\n\n<p><strong>b) <\/strong>10<\/p>\n\n\n\n<p><strong>c) <\/strong>15<\/p>\n\n\n\n<p><strong>d)<\/strong> 20<\/p>\n\n\n\n<p><strong>c)<\/strong> 25<\/p>\n\n\n\n<p><strong>Quest\u00e3o 4 &#8211;<\/strong> <strong><a href=\"http:\/\/www.uece.br\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(UECE 2010)<\/a> <\/strong>A idade de Paulo, em anos, \u00e9 um n\u00famero inteiro par que satisfaz a desigualdade x2 &#8211; 32x + 252 &lt; 0. O n\u00famero que representa a idade de Paulo pertence ao conjunto<\/p>\n\n\n\n<p><strong>a)<\/strong> {12, 13, 14}<\/p>\n\n\n\n<p><strong>b)<\/strong> {15, 16, 17}<\/p>\n\n\n\n<p><strong>c)<\/strong>{18, 19, 20}<\/p>\n\n\n\n<p><strong>d) <\/strong>{21, 22, 23}<\/p>\n\n\n\n<p><strong>Quest\u00e3o 6 &#8211; <a href=\"https:\/\/www.ifnmg.edu.br\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(IFNMG 2018)<\/a> <\/strong>A produ\u00e7\u00e3o sustent\u00e1vel tem se tornado a bandeira de muitas ind\u00fastrias, ressaltando o uso consciente dos recursos naturais em seus produtos. Uma empresa, que aderiu \u00e0 sustentabilidade, trabalha com a produ\u00e7\u00e3o de ta\u00e7as especiais e tem gastos fixos de R$ 200,00 mais o custo de R$ 2,00 por ta\u00e7a produzida. Sabendo-se que cada unidade ser\u00e1 vendida a R$ 10,00, quantas ta\u00e7as dever\u00e3o ser produzidas para que o valor arrecadado supere os gastos e gere menos impacto ao meio ambiente?<\/p>\n\n\n\n<p><strong>a)<\/strong> Mais de 25 ta\u00e7as<\/p>\n\n\n\n<p><strong>b)<\/strong> Entre 19 e 24 ta\u00e7as<\/p>\n\n\n\n<p><strong>c)<\/strong> Entre 15 e&nbsp; 18 ta\u00e7as<\/p>\n\n\n\n<p><strong>d) <\/strong>Menos de 15 ta\u00e7as<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Respostas dos exerc\u00edcios sobre de Inequa\u00e7\u00e3o do 1\u00b0 grau<\/h2>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 1 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>b)<\/strong> 0 &lt; x \u2264 4&nbsp;<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 2 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>c)<\/strong> x &lt; y<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 3 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>e)<\/strong> 25<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 4 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>b)<\/strong> {15, 16, 17}<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 5 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>a)<\/strong> Mais de 25 ta\u00e7as<\/p>\n\n\n\n<p>Estude para o Enem com o <a href=\"https:\/\/beduka.com\/simulado\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Simulado Beduka.<\/a> <strong>\u00c9 gratuito!<\/strong><\/p>\n\n\n\n<p>Gostou dos nossos Exerc\u00edcios de <strong>Inequa\u00e7\u00e3o do 1\u00b0 grau<\/strong>? Compartilhe com os seus amigos e comente abaixo sobre as \u00e1reas que voc\u00ea deseja mais explica\u00e7\u00f5es.<\/p>\n\n\n\n<p>Queremos te ajudar a encontrar a <strong>FACULDADE IDEAL! <\/strong>Logo abaixo, fa\u00e7a uma pesquisa por curso e cidade que te mostraremos todas as faculdades que podem te atender. <strong>Informamos a nota de corte, valor de mensalidade, nota do MEC, avalia\u00e7\u00e3o dos alunos, modalidades de ensino e muito mais.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Uma inequa\u00e7\u00e3o do primeiro grau \u00e9 respons\u00e1vel por expressar uma desigualdade. Ao contr\u00e1rio da equa\u00e7\u00e3o, ela n\u00e3o iguala uma opera\u00e7\u00e3o a zero, ela a coloca como \u201cmaior que\u201d, \u201cmenor que\u201d, \u201cMaior ou igual a\u201d ou \u201cmenor ou igual a\u201d. Leia o nosso resumo e coloque em pr\u00e1tica seu conhecimento com exerc\u00edcios de Inequa\u00e7\u00e3o do 1\u00b0 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":17557,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[610],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.10 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exerc\u00edcios de Inequa\u00e7\u00e3o do 1\u00b0 Grau com Gabarito<\/title>\n<meta name=\"description\" content=\"Lista de exerc\u00edcios de Inequa\u00e7\u00e3o do 1\u00b0 grau com foco no ENEM. 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