{"id":1524,"date":"2022-03-14T21:39:09","date_gmt":"2022-03-14T21:39:09","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseni-nerovnic-s-promennou-ve-jmenovateli\/"},"modified":"2022-03-15T21:11:03","modified_gmt":"2022-03-15T21:11:03","slug":"reseni-nerovnic-s-promennou-ve-jmenovateli","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseni-nerovnic-s-promennou-ve-jmenovateli\/","title":{"rendered":"\u0158e\u0161en\u00ed nerovnic s prom\u011bnnou ve jmenovateli"},"content":{"rendered":"<ul>\n<li>Speci\u00e1ln\u00edm p\u0159\u00edpadem nerovnic jsou ty, kter\u00e9 maj\u00ed prom\u011bnnou um\u00edst\u011bnou ve jmenovateli.<\/li>\n<li>Jak jsme si ji\u017e vysv\u011btlili, pokud je prom\u011bnn\u00e1 ve jmenovateli, nesm\u00edme celou nerovnici prom\u011bnnou vyn\u00e1sobit a t\u00edm se ji zbavit.<\/li>\n<li>Jak tedy takov\u00e9 nerovnice \u0159e\u0161it?<\/li>\n<li>Poj\u010fme si postup vysv\u011btlit na p\u0159\u00edkladu:<\/li>\n<\/ul>\n<p>$$\\frac{5}{x}+2&gt;4$$<\/p>\n<p>Za\u010dneme t\u00edm, \u017ee si pravou stranu p\u0159vedeme doleva tak, abychom na jedn\u00e9 stran\u011b dostali zlomek a na druh\u00e9 nulu<\/p>\n<p>$$\\frac{5}{x}+2&gt;4 \/ -4$$<\/p>\n<p>$$\\frac{5}{x}+2 -4&gt;4- 4$$<\/p>\n<p>$$\\frac{5}{x}-2&gt;0$$<\/p>\n<p>Nyn\u00ed mus\u00edme levou stranu upravit tak, abychom dostali jeden zlomek, tud\u00ed\u017e p\u0159evedeme v\u00fdraz spole\u010dn\u00e9ho jmenovatele:<\/p>\n<p>$$\\frac{5}{x}-2\\cdot\\frac{x}{x}&gt;0$$<\/p>\n<p>Tak z\u00edsk\u00e1me:<\/p>\n<p>$$\\frac{5-2x}{x}-&gt;0$$<\/p>\n<p>Nyn\u00ed se mus\u00edme zamyslet nad t\u00edm, kdy bude v\u00fdraz kladn\u00fd. Existuj\u00ed dv\u011b varianty:<\/p>\n<ol>\n<li>Kdy\u017e bude \u010ditatel i jmenovatel kladn\u00fd, nap\u0159\u00edklad: $$\\frac{3}{5}&gt;0$$<\/li>\n<li>Kdy\u017e bude \u010ditatel i jmenovatel z\u00e1porn\u00fd, nap\u0159\u00edklad: $$\\frac{-3}{-5}&gt;0$$<\/li>\n<\/ol>\n<p>Co z toho ted vypl\u00fdv\u00e1?<\/p>\n<p>Nerovnici mus\u00edme \u0159e\u0161it pro mo\u017enost, \u017ee je \u010ditatel i jmenovatel v\u011bt\u0161\u00ed jak nula a pro mo\u017enost, \u017ee je \u010ditatel i jmenovatel men\u0161\u00ed jak nula.<\/p>\n<p>\u0158e\u0161en\u00ed pro \u010ditatel i jmenovatel v\u011bt\u0161\u00ed jak nula:<\/p>\n<p>$${5-2x}&gt;0 \u2227 {x}-&gt;0$$<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1524","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0158e\u0161en\u00ed nerovnic s prom\u011bnnou ve jmenovateli | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseni-nerovnic-s-promennou-ve-jmenovateli\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0158e\u0161en\u00ed nerovnic s prom\u011bnnou ve jmenovateli | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Speci\u00e1ln\u00edm p\u0159\u00edpadem nerovnic jsou ty, kter\u00e9 maj\u00ed prom\u011bnnou um\u00edst\u011bnou ve jmenovateli. Jak jsme si ji\u017e vysv\u011btlili, pokud je prom\u011bnn\u00e1 ve jmenovateli, nesm\u00edme celou nerovnici prom\u011bnnou vyn\u00e1sobit a t\u00edm se ji zbavit. Jak tedy takov\u00e9 nerovnice \u0159e\u0161it? Poj\u010fme si postup vysv\u011btlit na p\u0159\u00edkladu: $$frac{5}{x}+2&gt;4$$ Za\u010dneme t\u00edm, \u017ee si pravou stranu p\u0159vedeme doleva tak, abychom na jedn\u00e9 ... 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Jak jsme si ji\u017e vysv\u011btlili, pokud je prom\u011bnn\u00e1 ve jmenovateli, nesm\u00edme celou nerovnici prom\u011bnnou vyn\u00e1sobit a t\u00edm se ji zbavit. Jak tedy takov\u00e9 nerovnice \u0159e\u0161it? Poj\u010fme si postup vysv\u011btlit na p\u0159\u00edkladu: $$frac{5}{x}+2&gt;4$$ Za\u010dneme t\u00edm, \u017ee si pravou stranu p\u0159vedeme doleva tak, abychom na jedn\u00e9 ... 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