{"id":5645,"date":"2022-02-21T02:41:19","date_gmt":"2022-02-20T18:41:35","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/arithmetic_and_geometric_sequences-2\/"},"modified":"2022-06-30T10:19:54","modified_gmt":"2022-06-30T02:19:54","slug":"inequalities_and_linear_programming","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/inequalities_and_linear_programming\/","title":{"rendered":"8. \u4e0d\u7b49\u5f0f\u8207\u7dda\u6027\u898f\u756b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"5645\" class=\"elementor elementor-5645\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-24bca577 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"24bca577\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-2c15826e\" data-id=\"2c15826e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-38e1270b elementor-widget elementor-widget-text-editor\" data-id=\"38e1270b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>8.0 \u6eab\u7fd2 \u4e0d\u7b49\u5f0f<\/h2><p>\u4e0d\u5c11\u540c\u5b78\u90fd\u6015\u505a \u4e0d\u7b49\u5f0f \u53ca\u7dda\u6027\u898f\u756b\u5605\u984c\u76ee\u3002<\/p><ul><li>\u7dda\u6027\u898f\u756b\uff0c\u56e0\u70baDSE\u6578\u5b78\u90fd\u597d\u5c11\u51fa\uff0c\u6240\u4ee5\u5982\u679c\u4f60\u5514\u4fc2\u8ad7\u4f4f\u651e5*\/5**, \u5514\u8b58\/\u5514\u7406\u4f62\u5176\u5be6\u90fd\u5514\u6703\u6709\u592a\u5927\u5605\u5f71\u97ff\u3002<\/li><li>\u81f3\u65bc\u4e0d\u7b49\u5f0f, \u56e0\u70ba\u505a\u4e0d\u7b49\u5f0f\u5605\u6578\u4fc2\u540c\u505a\u89e3\u65b9\u7a0b\u5605\u6578\u5dee\u4e0d\u591a, \u53ea\u4fc2\u591a\u5497\u4e00\u3001\u5169\u500b\u6280\u5de7\u8981\u53bb\u5b78\u540c\u7559\u610f\uff0c\u800c\u4e14\u90fd\u6709\u56fa\u5b9a\u5481\u51fa\uff0c\u6240\u4ee5\u5efa\u8b70\u5927\u5bb6\u53bb\u6eab\u4e00\u6eab\u3002<\/li><\/ul><p>\u672a\u5b78\u65b0\u5622\u524d\uff0c\u6211\u5730\u5148\u569f\u6eab\u4e00\u6eab\u521d\u4e2d\u5b78\u904e\u5605\u4e0d\u7b49\u5f0f\u77e5\u8b58\u5148\u3002<\/p><h3 style=\"text-align: center;\"><span style=\"color: #ff0000;\">\u4e0d\u7b49\u5f0f \u4fc2\u4e00\u500b\u8868\u793a\u201c\u4e0d\u76f8\u7b49\u95dc\u4fc2\u201d\u5605\u6578\u5f0f\u3002<\/span><\/h3><ul><li>\u800c\u201c\u4e0d\u76f8\u7b49\u201d\u53ef\u4ee5\u5206\u6210\u56db\u7a2e\u60c5\u6cc1\uff1a<ul><li>&gt;\uff1a\u5927\u904e<\/li><li>&lt;\uff1a\u7d30\u904e<\/li><li>\u2265\uff1a\u5927\u904e\u6216\u7b49\u65bc<\/li><li>\u2264\uff1a\u7d30\u904e\u6216\u7b49\u65bc<\/li><li>\u00a0<\/li><\/ul><\/li><\/ul><h3>8.0.1 \u89e3\u8b80 \u4e0d\u7b49\u5f0f<\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-db056ae elementor-widget elementor-widget-accordion\" data-id=\"db056ae\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2291\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2291\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">\u4f8b\u5b501\uff1a x > 5<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2291\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2291\"><ul><li>\u4f9d\u500b\u4e0d\u7b49\u5f0f\u8b80\u4f5c \u201cx \u5927\u904e 5\u201d\u3002<\/li><li>\u7559\u610f\u4e0d\u7b49\u5f0f\u4fc2\u5514\u6703\u8a71\u6bd4\u6211\u54cb\u77e5x\u5230\u5e95\u4fc2\u5e7e\u591a\u3002<ul><li>\u6211\u54cb\u53ea\u4fc2\u77e5\u9053 \u201cx\u7684\u53ef\u80fd\u7bc4\u570d\u201d\u3002<\/li><li>\u56e0\u70ba x \u5927\u904e5\uff0c\u6240\u4ee5x\u7684\u503c\u53ef\u80fd\u662f6\u30018\u300110.1\u2026\u2026<ul><li>\u7e3d\u4e4b\u5927\u904e5\u5c31\u5f97\u3002<\/li><\/ul><\/li><\/ul><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2292\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2292\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">\u4f8b\u5b502\uff1a 5 > x<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2292\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2292\"><ul><li>\u4f9d\u500b\u4f8b\u5b50\u540c\u4f8b\u5b501\u7747\u843d\u597d\u4f3c\u5dee\u4e0d\u591a\uff0c\u53ea\u4fc2x\u540c5\u63db\u5497\u4f4d\u3002<ul><li>\u4f46\u500b\u610f\u7fa9\u5c31\u7d55\u5c0d\u5514\u540c\u3002<\/li><\/ul><\/li><li>\u540c\u5b78\u4e00\u822c\u6703\u8b80\u6210\u201c5\u5927\u904ex\u201d\u3002\u4f46\u6211\u5efa\u8b70\u5148\u7531x\u958b\u59cb\u8b80\u8d77\u3002<ul><li>\u6240\u4ee5\u4eca\u6b21\u8981\u7531\u53f3\u81f3\u5de6\uff0c\u8b80\u4f5c\u201cx\u7d30\u904e5\u201d\uff08\u7559\u610f\u56e0\u7b26\u865f\u7d30D\u55f0\u908a\u6bd4\u8f03\u8fd1x\uff0c\u6240\u4ee5\u4fc2\u8b80\u6210\u201c\u7d30\u904e\u201d\uff09\u3002<\/li><\/ul><\/li><li>\u9ede\u89e3\u8981\u5481\u505a\uff1f\u56e0\u70ba\u6211\u54cb\u901a\u5e38\u60f3\u77e5x\u4fc2\u5927\u904e\u5b9a\u7d30\u904e\u54a9\u6578\uff0c\u800c\u5514\u4fc2\u67d0\u6578\u5927\u904e\u5b9a\u7d30\u904ex\u3002<\/li><li>\u53e6\u5916\u6211\u54cb\u901a\u5e38\u4fc2\u6703\u5c07x\u5beb\u55ba\u5de6\u908a\u3002\u7fd2\u6163\u4f9d\u500b\u8b80\u6cd5\u4e4b\u5f8c\uff0c\u6211\u54cb\u53ea\u8981\u55ba\u4e0b\u4e00\u884c\u5c07\u500b\u8b80\u6cd5\u5beb\u4e00\u6b21\u5c31\u5f97\u3002\u5373\u201cx\u7d30\u904e5\u201d\u53ef\u5beb\u6210\uff1a<ul><li>x &lt; 5<\/li><\/ul><\/li><\/ul><p>\u61c9\u7528\uff1a -5 \u2264 x \u53ef\u4ee5\u8b80\u6210\u201cx\u5927\u904e\u6216\u5b9a\u65bc-5\u201d\u3002<br \/>\u6240\u4ee5\u53ef\u5beb\u6210\uff1a x \u2265 -5<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b5f19d5 elementor-widget elementor-widget-text-editor\" data-id=\"b5f19d5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>8.0.2 \u89e3\u4e00\u5143\u4e00\u6b21\u4e0d\u7b49\u5f0f<\/h3><ul><li>\u5148\u91cd\u6eab\u54a9\u53eb\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u3002<ul><li>\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u500b\u6a23\u4fc2\u5481\u5605\uff1a 3x \u2013 5 = 8<\/li><li>\u5176\u5be6\u9664\u5497\u500b\u540d\u5927\u5bb6\u53ef\u80fd\u5514\u719f\u4e4b\u5916\uff0c\u771f\u4fc2\u7121\u54a9\u7279\u5225\u3002<\/li><\/ul><\/li><\/ul><ul><li>\u800c \u4e00\u5143\u4e00\u6b21\u4e0d\u7b49\u5f0f \u53ea\u4fc2\u5c07\u500b\u201c\uff1d\u201d\u865f\u8b8a\u70ba\u201c\u4e0d\u7b49\u5f0f\u7b26\u865f\u201d (\u5373 &gt;, &lt; \u7b49)\u3002<\/li><\/ul><p>\u800c\u89e3\u4e00\u5143\u4e00\u6b21\u4e0d\u7b49\u5f0f\u5605<span style=\"color: #ff0000;\">\u6280\u5de7\uff1a<\/span><\/p><ul><li><span style=\"color: #ff0000;\">\u57fa\u672c\u4e0a\u540c\u89e3\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u76f8\u540c<\/span><\/li><li><span style=\"color: #ff0000;\">\u552f\u4e00\u5514\u540c\u5605\u4fc2\uff1a<\/span><br \/><span style=\"color: #ff0000;\">\u7576\u6211\u54cb\u5c07\u689d\u5f0f\u201c\u4e58\u201d\u6216\u201c\u9664\u201d\u4e00\u500b\u8ca0\u6578\u6642\uff0c\u8981\u5c07\u500b\u201c\u4e0d\u7b49\u5f0f\u7b26\u865f\u201d\u8fd4\u8f49<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8ac62eb elementor-widget elementor-widget-accordion\" data-id=\"8ac62eb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1451\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1451\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">\u89e3\u8aaa1\uff1a \u6bd4\u8f03\u89e3\u4ee5\u4e0b\u7684\u4e0d\u7b49\u5f0f\u548c\u65b9\u7a0b<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1451\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1451\"><p>\\(\\begin{align}<br \/>3x+2 &amp;&gt; 8\u00a0 \u00a0\\quad &amp; \\quad\u00a0 3x + 2 &amp;= 8 \\\\<br \/>3x &amp;&gt; 8\u20132 \u00a0\\quad &amp; \\quad\u00a0 \u00a0 \u00a03x &amp;= 8-2 \\\\<br \/>3x &amp;&gt; 6 \u00a0\\quad &amp; \\quad\u00a0 \u00a0 3x &amp;= 6 \\\\<br \/>x &amp;&gt; 6 \/ 3 \u00a0\\quad &amp; \\quad\u00a0 \u00a0 x &amp;= 6\/ 3 \\\\<br \/>x &amp;&gt; 2 \u00a0\\quad &amp; \\quad\u00a0 \u00a0 x &amp;= 2<br \/>\\end{align}\\)<\/p><p>\u5e0c\u671b\u540c\u5b78\u53ef\u4ee5\u7747\u5230\u89e3\u4e0d\u7b49\u5f0f\u540c\u89e3\u65b9\u7a0b\u5605\u6280\u5de7\u4fc2\u4f3c\u5230\u5341\u8db3\u3002<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1452\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-1452\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">\u89e3\u8aaa2\uff1a \u518d\u6bd4\u8f03\u89e3\u4ee5\u4e0b\u7684\u4e0d\u7b49\u5f0f\u548c\u65b9\u7a0b<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1452\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-1452\"><p>\\(\\begin{align}<br \/>-3x+2 &amp;&gt; 8\u00a0 \u00a0\\quad &amp; \\quad\u00a0 -3x + 2 &amp;= 8 \\\\<br \/>-3x &amp;&gt; 8\u20132 \u00a0\\quad &amp; \\quad\u00a0 \u00a0 \u00a0-3x &amp;= 8-2 \\\\<br \/>-3x &amp;&gt; 6 \u00a0\\quad &amp; \\quad\u00a0 \u00a0 -3x &amp;= 6 \\\\<br \/>x &amp;&lt; 6 \/ (-3)\u00a0 \\quad &amp; \\quad\u00a0 \u00a0 x &amp;= 6\/ (-3) \\\\<br \/>x &amp;&lt; -2 \u00a0\\quad &amp; \\quad\u00a0 \u00a0 x &amp;= -2<br \/>\\end{align}\\)<\/p><p><br 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