{"id":1494,"date":"2022-03-14T13:41:36","date_gmt":"2022-03-14T13:41:36","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/linearni-nerovnice\/"},"modified":"2022-03-14T15:06:28","modified_gmt":"2022-03-14T15:06:28","slug":"linearni-nerovnice","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/linearni-nerovnice\/","title":{"rendered":"Line\u00e1rn\u00ed nerovnice"},"content":{"rendered":"<ul>\n<li>Existuj\u00ed dva typy nerovnic. Prvn\u00edm typem jsou nerovnice line\u00e1rn\u00ed.<\/li>\n<li>Ty maj\u00ed tvar:<\/li>\n<\/ul>\n<p style=\"text-align: center\"><em><strong>ax + b&gt;0<\/strong><\/em><\/p>\n<p style=\"text-align: center\"><em><strong>ax + b\u22650<\/strong><\/em><\/p>\n<p style=\"text-align: center\"><em><strong>ax + b&lt;0<\/strong><\/em><\/p>\n<p style=\"text-align: center\"><em><strong>ax + b\u22640<\/strong><\/em><\/p>\n<ul>\n<li style=\"text-align: left\">Poj\u010fme si line\u00e1rn\u00ed nerovnici uk\u00e1zat a rovnou ji vy\u0159e\u0161it:<\/li>\n<\/ul>\n<p>$$2x + 4 &gt; 5$$<\/p>\n<p>Za\u010dneme t\u00edm, \u017ee si v\u00fdraz s x nech\u00e1me vlevo a 4 p\u0159esuneme vpravo,<\/p>\n<p>$$2x + 4 -4 &gt; 5 &#8211; 4$$<\/p>\n<p>$$2x &gt; 1$$<\/p>\n<p>Nyn\u00ed se zbav\u00edme dvojky tak, \u017ee celou nerovnici vyd\u011bl\u00edme dv\u011bma<\/p>\n<p>$$2x : 2 &gt; 1 : 2$$<\/p>\n<p>Dostaneme:<\/p>\n<p>$$x&gt;\\frac{1}{2}$$<\/p>\n<p>P\u0159i po\u010d\u00edt\u00e1n\u00ed rovnic by byl toto n\u00e1\u0161 v\u00fdsledek. My ale po\u010d\u00edt\u00e1me nerovnice, tud\u00ed\u017e v\u00edme, \u017ee <strong>v\u00fdsledkem m\u016f\u017ee b\u00fdt jak\u00e9koliv \u010d\u00edslo, kter\u00e9 je v\u011bt\u0161\u00ed ne\u017e jedna polovina<\/strong>. To znamen\u00e1, \u017ee<strong> v\u00fdsledkem je interval od jedn\u00e9 poloviny do nekone\u010dna<\/strong>. V\u00fdsledek tedy zap\u00edeme takto:<\/p>\n<p>$$K=(\\frac{1}{2};\u221e)$$<\/p>\n<p>Proto\u017ee v nerovnosti bylo znam\u00e9nko &gt; (a nikoliv znamenko \u2265). <strong>Interval bude u jedn\u00e9 poloviny otev\u0159en\u00fd,<\/strong> proto\u017ee jedna polovina do intervalu v\u00fdsledk\u016f nespad\u00e1.<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1494","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>Line\u00e1rn\u00ed nerovnice | 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\/linearni-nerovnice\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Line\u00e1rn\u00ed nerovnice | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Existuj\u00ed dva typy nerovnic. Prvn\u00edm typem jsou nerovnice line\u00e1rn\u00ed. Ty maj\u00ed tvar: ax + b&gt;0 ax + b\u22650 ax + b&lt;0 ax + b\u22640 Poj\u010fme si line\u00e1rn\u00ed nerovnici uk\u00e1zat a rovnou ji vy\u0159e\u0161it: $$2x + 4 &gt; 5$$ Za\u010dneme t\u00edm, \u017ee si v\u00fdraz s x nech\u00e1me vlevo a 4 p\u0159esuneme vpravo, $$2x + 4 -4 ... 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Prvn\u00edm typem jsou nerovnice line\u00e1rn\u00ed. Ty maj\u00ed tvar: ax + b&gt;0 ax + b\u22650 ax + b&lt;0 ax + b\u22640 Poj\u010fme si line\u00e1rn\u00ed nerovnici uk\u00e1zat a rovnou ji vy\u0159e\u0161it: $$2x + 4 &gt; 5$$ Za\u010dneme t\u00edm, \u017ee si v\u00fdraz s x nech\u00e1me vlevo a 4 p\u0159esuneme vpravo, $$2x + 4 -4 ... 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