{"id":126544,"date":"2017-08-30T11:30:13","date_gmt":"2017-08-30T13:30:13","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=126544"},"modified":"2026-05-26T16:12:35","modified_gmt":"2026-05-26T18:12:35","slug":"inequacao-do-1o-grau","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/inequacao-do-1o-grau","title":{"rendered":"Inequa\u00e7\u00e3o do 1\u00ba Grau"},"content":{"rendered":"

Uma\u00a0inequa\u00e7\u00e3o do 1\u00ba grau\u00a0<\/b>\u00e9 uma afirma\u00e7\u00e3o matem\u00e1tica que expressa uma desigualdade linear. Ela utiliza os s\u00edmbolos >\u00a0 (maior que), < (menor que), \u2265\u00a0 (maior ou igual a) ou \u2265\u00a0 (menor ou igual a), e a inc\u00f3gnita (geralmente x) possui expoente 1\\. A resolu\u00e7\u00e3o \u00e9 parecida com a de uma equa\u00e7\u00e3o, resultando em um intervalo de valores.<\/p>\n

Chamamos de\u00a0<\/b>Inequa\u00e7\u00e3o do 1\u00ba Grau<\/strong>\u00a0na vari\u00e1vel x a desigualdade que pode ser representada nas formas:<\/b><\/p>\n

ax + b < 0
\nax + b\u00a0\u2264 0
\nax + b > 0
\nax + b\u00a0\u2265 0
\nax + b\u00a0\u2260 0<\/p>\n

onde\u00a0a<\/em>\u00a0e\u00a0b<\/em>\u00a0s\u00e3o constantes reais, com\u00a0a<\/em>\u00a0\u2260 0.<\/p>\n

Ou seja, a inequa\u00e7\u00e3o nada mais \u00e9 que uma senten\u00e7a que possui um conjunto solu\u00e7\u00e3o. S\u00e3o utilizadas para indicarem uma desigualdade, seja ela alg\u00e9brica ou num\u00e9rica.<\/p>\n

Nas equa\u00e7\u00f5es temos uma igualdade, pois buscamos que dois valores sejam iguais. J\u00e1 as inequa\u00e7\u00f5es s\u00e3o desigualdades, e o interessante \u00e9 descobrir, por exemplo, dentre muitas op\u00e7\u00f5es, quais delas oferecem o melhor custo-benef\u00edcio.<\/p>\n

Ent\u00e3o, por esse motivo que ao inv\u00e9s do s\u00edmbolo de igual \u201c=\u201d utiliza-se os s\u00edmbolos:<\/b>\u00a0\u201c<\u201c, \u201c\u2264\u201d, \u201c>\u201d, \u201c\u2265\u201d.<\/p>\n

S\u00edmbolos da Inequa\u00e7\u00e3o<\/b><\/p>\n

Como j\u00e1 falamos, nas inequa\u00e7\u00f5es podemos utilizar os seguintes s\u00edmbolos:<\/strong><\/p>\n

< \u2192 menor que;
\n\u2264 \u2192 menor ou igual que;
\n> \u2192 maior que;
\n\u2265 \u2192 maior ou igual que;<\/p>\n

Propriedades da Inequa\u00e7\u00e3o<\/b><\/p>\n

Sejam as express\u00f5es A, B, C e D.<\/p>\n

1)<\/strong>\u00a0Se A\u00a0\u2264 B, ent\u00e3o B\u00a0\u2265 A;
\n2)<\/strong>\u00a0Se\u00a0A\u00a0\u2264 B e B\u00a0\u2264 C, ent\u00e3o A\u00a0\u2264 C;
\n3)<\/strong>\u00a0Se A\u00a0\u2264 B, ent\u00e3o A + C\u00a0\u2264 B + C;
\n4)<\/strong>\u00a0Se C > 0 e A\u00a0\u2264 B, ent\u00e3o CA\u00a0\u2264 CB;
\n5)<\/strong>\u00a0Se C < 0 e A\u00a0\u2264 B, ent\u00e3o CA \u2265 CB;
\n6)<\/strong>\u00a0Se A\u00a0\u2264 B e C\u00a0\u2264 D, ent\u00e3o A + C\u00a0\u2264 B + D;<\/p>\n

Exemplos<\/strong><\/p>\n

1)<\/strong>\u00a05x \u2013 12 \u2264 0<\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/p>\n

\"inequacao-do-1o-grau-1\"<\/p>\n

2)<\/strong> 2x\/3 + 6\u00a0\u2265 x\/5 + 9<\/p>\n

Resolu\u00e7\u00e3o:<\/p>\n

\"inequacao-do-1o-grau-2\"<\/p>\n

Fonte:<\/strong>\u00a0Portal S\u00e3o Francisco<\/p>\n","protected":false},"excerpt":{"rendered":"

Uma\u00a0inequa\u00e7\u00e3o do 1\u00ba grau\u00a0\u00e9 uma afirma\u00e7\u00e3o matem\u00e1tica que expressa uma desigualdade linear. Ela utiliza os s\u00edmbolos >\u00a0 (maior que), < (menor que), \u2265\u00a0 (maior ou igual a) ou \u2265\u00a0 (menor ou igual a), e a inc\u00f3gnita (geralmente x) possui expoente 1\\. A resolu\u00e7\u00e3o \u00e9 parecida com a de uma equa\u00e7\u00e3o, resultando em um intervalo de […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-126544","post","type-post","status-publish","format-standard","hentry","category-matematica"],"acf":[],"yoast_head":"\nInequa\u00e7\u00e3o do 1\u00ba Grau, Matem\u00e1tica Inequa\u00e7\u00e3o do 1\u00ba Grau<\/title>\n<meta name=\"description\" content=\"Inequa\u00e7\u00e3o do 1\u00ba Grau, Matem\u00e1tica, Vari\u00e1vel, Desigualdade, Conjunto, Valores, S\u00edmbolos, Propriedades, Exemplo, Inequa\u00e7\u00e3o do 1\u00ba Grau\" \/>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" 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