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A critical thinking question (11) asks students to write a rational inequality whose solution matches a specified interval set. Designed for practice in Infinite Precalculus, focusing on analyzing inequalities involving rational expressions.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/rational-inequalities-solve-each-inequality/523491/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/rational-inequalities-solve-each-inequality/523491.png","ImageObject",300,407,{"name":92,"@type":93},"PakDamar76","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What do problems 1 through 10 require students to do?","Question",{"text":113,"@type":114},"Solve each rational inequality and express the solution set using interval notation.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the solution set represented on this worksheet?",{"text":118,"@type":114},"Using interval notation with parentheses or brackets, including unions of intervals where applicable.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the goal of the critical thinking question (11)?",{"text":122,"@type":114},"Write a rational inequality that has the given solution set, specifically a union of intervals.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},523491,1791504289,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":24,"preview_page_count":4},962090893057,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Precalculus Rational Inequalities  \nName  Date  Period   \nSolve each inequality.  \n1) xx~~ ~~􀀐~~ ~~􀀚􀀔~~ ~~ 􀀟 􀀓 2) xx~~ ~~~~ ~~􀀘􀀗 􀁤 􀀓  \nx 􀀎 􀀖􀀕   x 􀀎 􀀙􀀛   \n3) 􀁤 􀀖 4) 􀁴 􀀘 x 􀀎 􀀙 x 􀀎 􀀛  \n5) (x~~ ~~􀀎~~ ~~(􀀎~~ ~~􀀘~~ ~~) 􀁴 􀀓 6) x~~ 􀀕 ~~􀀐x􀀎􀀘x􀀙􀀐~~ ~~􀀕􀀗~~ ~~ 􀁴 􀀓  \n7) 􀀐 ~~ ~~x~~ ~~~~ ~~􀀘~~ ~~ 􀁴 􀀐 ~~ ~~x~~ ~~~~ ~~􀀙~~ ~~ 8) 􀀐 ~~ ~~x~~ ~~~~ ~~􀀚~~ ~~ 􀁤 􀀐 ~~ ~~x~~ ~~~~ ~~􀀛~~ ~~  \n9) 􀀐 ~~ ~~x~~ ~~􀀚􀀎~~ ~~􀀘~~ ~~ 􀁤 􀀐 ~~ ~~x~~ ~~~~ ~~􀀙~~ ~~ 10) (x~~ ~~􀀎~~(~~x􀀚x􀀘~~)~~~~ ~~􀀖) 􀀡 􀀓  \nCritical thinking question:  \n11) Write a rational inequality with the solution: (􀀐􀀕 , 􀀐􀀔) ∪(􀀔 , 􀁦)  \nKuta Software-Infinite Precalculus Name   \nRational Inequalities Date  Period   \nSolve each inequality.  \n1) xx~~ ~~􀀐~~ ~~􀀚􀀔~~ ~~ 􀀟 􀀓 2) xx~~ ~~~~ ~~􀀘􀀗 􀁤 􀀓  \n(􀀔 , 􀀚 ) [􀀐􀀘 , 􀀗)  \n3) xx􀀎􀀎􀀖􀀕􀀙~~ ~~ 􀁤 􀀖 4) xx􀀎􀀎􀀙􀀛􀀛~~ ~~ 􀁴 􀀘  \n(􀀐􀁦 , 􀀐􀀙) ∪ [􀀚 , 􀁦) (􀀐􀀛 , 􀀚 ]  \n5) (x~~ ~~􀀎~~ ~~(􀀎~~ ~~􀀘~~ ~~) 􀁴 􀀓 6) x~~ 􀀕 ~~􀀐x􀀎􀀘x􀀙􀀐~~ ~~􀀕􀀗~~ ~~ 􀁴 􀀓  \n[􀀐􀀘 , 􀀐􀀖] ∪(􀀐􀀕 , 􀁦) [􀀐􀀙 , 􀀐􀀖) ∪(􀀛 , 􀁦)  \n7) 􀀐 ~~ ~~x~~ ~~~~ ~~􀀘~~ ~~ 􀁴 􀀐 ~~ ~~x~~ ~~~~ ~~􀀙~~ ~~ 8) 􀀐 ~~ ~~x~~ ~~~~ ~~􀀚~~ ~~ 􀁤 􀀐 ~~ ~~x~~ ~~~~ ~~􀀛~~ ~~  \n[􀀐􀀘 , 􀀘 ) ∪(􀀙 , 􀁦) (􀀐􀁦 , 􀀐􀀛) ∪(􀀐􀀚 , 􀀐􀀗]  \n9) 􀀐 ~~ ~~x~~ ~~􀀚􀀎~~ ~~􀀘~~ ~~ 􀁤 􀀐 ~~ ~~x~~ ~~~~ ~~􀀙~~ ~~ 10) (x~~ ~~􀀎~~(~~x􀀚x􀀘~~)~~~~ ~~􀀖) 􀀡 􀀓  \n(􀀐􀁦 , 􀀐􀀙) ∪(􀀐􀀘 , 􀀕] (􀀐􀁦 , 􀀐􀀚) ∪(􀀖 , 􀀘 ) ∪(􀀘 , 􀁦)  \nCritical thinking question:  \n11) Write a rational inequality with the solution: (􀀐􀀕 , 􀀐􀀔) ∪(􀀔 , 􀁦)  \nExample: ~~ ~~(x~~ ~~􀀎~~ ~~~~ ~~(~~ ~~􀀎~~ ~~􀀕) 􀀡 􀀓  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiicGLW7YoTBG","https://ap.wps.com/l/cbCaiicGLW7YoTBG","pdf",43215,"English","# Solve each inequality\n## Problems 1-10\n## Critical thinking question 11","[{\"question\":\"What do problems 1 through 10 require students to do?\",\"answer\":\"Solve each rational inequality and express the solution set using interval notation.\"},{\"question\":\"How is the solution set represented on this worksheet?\",\"answer\":\"Using interval notation with parentheses or brackets, including unions of intervals where applicable.\"},{\"question\":\"What is the goal of the critical thinking question (11)?\",\"answer\":\"Write a rational inequality that has the given solution set, specifically a union of intervals.\"}]","Rational Inequalities - Solve each inequality | PDF",1791426914]