{"id":296794,"date":"2022-09-10T20:40:38","date_gmt":"2022-09-10T15:10:38","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/let-ax%e2%88%88rx3x4%e2%89%a43-and-bx%e2%88%88r3x%e2%88%91r1%e2%88%9e%e2%80%8a310rx%e2%88%923\/"},"modified":"2022-09-10T20:40:38","modified_gmt":"2022-09-10T15:10:38","slug":"let-ax%e2%88%88rx3x4%e2%89%a43-and-bx%e2%88%88r3x%e2%88%91r1%e2%88%9e%e2%80%8a310rx%e2%88%923","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/letaxrx3x43andbxr3xr1310rx333xthe\/","title":{"rendered":"Let\u00a0A={x\u2208R:[x+3]+[x+4]\u22643}\u00a0and\u00a0B=x\u2208R:3x\u2211r=1\u221e\u200a310rx\u22123<3\u22123x\u00a0then"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Let\u00a0A={x\u2208R:[x+3]+[x+4]\u22643}\u00a0and\u00a0B=x\u2208R:3x\u2211r=1\u221e\u200a310rx\u22123&lt;3\u22123x\u00a0then","custom_permalink":"question\/mathematics\/letaxrx3x43andbxr3xr1310rx333xthe\/"},"categories":[],"acf":{"question":"<p>Let&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mo>=<\/mo><mo>{<\/mo><mi>x<\/mi><mo>\u2208<\/mo><mi mathvariant=\"bold\">R<\/mi><mo>:<\/mo><mo>[<\/mo><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mo>]<\/mo><mo>+<\/mo><mo>[<\/mo><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mo>]<\/mo><mo>\u2264<\/mo><mn>3<\/mn><mo>}<\/mo><\/math>&nbsp;and&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>B<\/mi><mo>=<\/mo><mfenced separators=\"|\" close=\"}\" open=\"{\"><mrow><mi>x<\/mi><mo>\u2208<\/mo><mi mathvariant=\"bold\">R<\/mi><mo>:<\/mo><msup><mn>3<\/mn><mi>x<\/mi><\/msup><msup><mfenced separators=\"|\"><mrow><munderover><mo>\u2211<\/mo><mrow><mi>r<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi mathvariant=\"normal\">\u221e<\/mi><\/munderover><mo>\u200a<\/mo><mfrac><mn>3<\/mn><msup><mn>10<\/mn><mi>r<\/mi><\/msup><\/mfrac><\/mrow><\/mfenced><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>&lt;<\/mo><msup><mn>3<\/mn><mrow><mo>\u2212<\/mo><mn>3<\/mn><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mfenced><\/math>&nbsp;then<\/p>","options":[{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mo>&nbsp;<\/mo><mo>=<\/mo><mo>&nbsp;<\/mo><mi>B<\/mi><\/math><\/p>","correct":true},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mo>\u2acb<\/mo><mi>B<\/mi><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>B<\/mi><mo>\u228a<\/mo><mi>A<\/mi><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo>=<\/mo><mi>\u03d5<\/mi><\/math><\/p>","correct":false}],"solution":"<p>Let&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>\u2208<\/mo><mi>A<\/mi><mo>,<\/mo><mo>[<\/mo><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mo>]<\/mo><mo>+<\/mo><mo>[<\/mo><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mo>]<\/mo><mo>\u2264<\/mo><mn>3<\/mn><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"center left\" columnspacing=\"1em\"><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><\/mtd><mtd><mo>[<\/mo><mi>x<\/mi><mo>]<\/mo><mo>+<\/mo><mn>3<\/mn><mo>+<\/mo><mo>[<\/mo><mi>x<\/mi><mo>]<\/mo><mo>+<\/mo><mn>4<\/mn><mo>\u2264<\/mo><mn>3<\/mn><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><\/mtd><mtd><mn>2<\/mn><mo>[<\/mo><mi>x<\/mi><mo>]<\/mo><mo>\u2264<\/mo><mo>\u2212<\/mo><mn>4<\/mn><mo stretchy=\"false\">\u21d2<\/mo><mo>[<\/mo><mi>x<\/mi><mo>]<\/mo><mo>\u2264<\/mo><mo>\u2212<\/mo><mn>2<\/mn><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><\/mtd><mtd><mi>x<\/mi><mo>\u2208<\/mo><mo>(<\/mo><mo>\u2212<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo>,<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo>)<\/mo><\/mtd><\/mtr><mtr><mtd>&nbsp;<\/mtd><mtd><mi>A<\/mi><mo>=<\/mo><mo>(<\/mo><mo>\u2212<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo>,<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo>)<\/mo><\/mtd><\/mtr><\/mtable><\/math><\/p><p>If&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>&nbsp;<\/mo><mo>\u2208<\/mo><mo>&nbsp;<\/mo><mi>B<\/mi><\/math>&nbsp;then&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mn>3<\/mn><mi>x<\/mi><\/msup><msup><mn>3<\/mn><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><msup><mfenced separators=\"|\"><mrow><munderover><mo>\u2211<\/mo><mrow><mi>r<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi mathvariant=\"normal\">\u221e<\/mi><\/munderover><mo>\u200a<\/mo><mfrac><mn>1<\/mn><msup><mn>10<\/mn><mi>r<\/mi><\/msup><\/mfrac><\/mrow><\/mfenced><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>&lt;<\/mo><msup><mn>3<\/mn><mrow><mo>\u2212<\/mo><mn>3<\/mn><mi>x<\/mi><\/mrow><\/msup><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"left left\" columnspacing=\"1em\"><mtr><mtd><mrow><mo stretchy=\"false\">\u21d2<\/mo><mspace width=\"1em\">&nbsp;<\/mspace><mo>\u2005\u2005\u2005\u2005<\/mo><\/mrow><msup><mn>3<\/mn><mrow><mn>2<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><msup><mfenced separators=\"|\"><mfrac><mrow><mn>1<\/mn><mo>\/<\/mo><mn>10<\/mn><\/mrow><mrow><mn>1<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>\/<\/mo><mn>10<\/mn><\/mrow><\/mfrac><\/mfenced><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>&lt;<\/mo><msup><mn>3<\/mn><mrow><mo>\u2212<\/mo><mn>3<\/mn><mi>x<\/mi><\/mrow><\/msup><\/mtd><\/mtr><mtr><mtd><mrow><mo stretchy=\"false\">\u21d2<\/mo><mspace width=\"1em\">&nbsp;<\/mspace><mo>\u2005\u2005\u2005\u2005<\/mo><\/mrow><msup><mn>3<\/mn><mrow><mn>2<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><msup><mfenced separators=\"|\"><msup><mn>3<\/mn><mrow><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mfenced><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>&lt;<\/mo><msup><mn>3<\/mn><mrow><mo>\u2212<\/mo><mn>3<\/mn><mi>x<\/mi><\/mrow><\/msup><\/mtd><\/mtr><mtr><mtd><mrow><mo stretchy=\"false\">\u21d2<\/mo><mspace width=\"1em\">&nbsp;<\/mspace><mo>\u2005\u2005\u2005\u2005<\/mo><\/mrow><mrow><msup><mn>3<\/mn><mn>3<\/mn><\/msup><mo>&lt;<\/mo><msup><mn>3<\/mn><mrow><mo>\u2212<\/mo><mn>3<\/mn><mi>x<\/mi><\/mrow><\/msup><mo stretchy=\"false\">\u21d2<\/mo><mn>3<\/mn><mo>&lt;<\/mo><mo>\u2212<\/mo><mn>3<\/mn><mi>x<\/mi><\/mrow><\/mtd><\/mtr><mtr><mtd><mo>\u2005\u2005\u2005\u2005<\/mo><mrow><mtext>so&nbsp;<\/mtext><mi>x<\/mi><mo>\u2208<\/mo><mo>(<\/mo><mo>\u2212<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo>,<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/p><p>Hence&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>B<\/mi><mo>=<\/mo><mo>(<\/mo><mo>\u2212<\/mo><mi mathvariant=\"normal\">\u221e<\/mi><mo>,<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo>)<\/mo><\/math>&nbsp;<\/p><p>Thus&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mo>&nbsp;<\/mo><mo>=<\/mo><mo>&nbsp;<\/mo><mi>B<\/mi><\/math>.<\/p>","subject":""},"yoast_head":"<!-- This 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