[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-207092-105":3,"detail-sidebar-cat-0-en-105":74,"doc-detail-207092-en":124},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":67,"head_meta":69,"extra_data":71,"updated_unix":73},105,"en","graphing-inequalities-finding-regions-using-inequalities","Graphing Inequalities - Finding Regions using Inequalities","","Revision notes explaining how to graph inequalities and interpret inequalities on coordinate graphs. The material shows how to draw each boundary line using straight line knowledge, selecting solid lines for inclusive ≤ or ≥ and dotted lines for exclusive \u003C or >. It guides deciding which side of each line to shade by testing points, then combining shaded regions. Worked examples demonstrate labeling and determining maximum and minimum points within inequality-defined regions.",{"@graph":14,"@context":66},[15,34,49],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/graphing-inequalities-finding-regions-using-inequalities/207092/",4,{"url":32,"name":10,"@type":35,"author":36,"headline":10,"publisher":39,"fileFormat":42,"inLanguage":8,"description":12,"dateModified":43,"datePublished":43,"encodingFormat":42,"isAccessibleForFree":44,"interactionStatistic":45},"DigitalDocument",{"name":37,"@type":38},"Quinn","Person",{"url":19,"name":40,"@type":41},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":46,"interactionType":47,"userInteractionCount":4},"InteractionCounter",{"@type":48},"ViewAction",{"@type":50,"mainEntity":51},"FAQPage",[52,58,62],{"name":53,"@type":54,"acceptedAnswer":55},"How do you decide whether a boundary line should be solid or dotted when graphing an inequality?","Question",{"text":56,"@type":57},"Use a solid line for ≤ or ≥ (the line is included) and a dotted line for \u003C or > (the line is not included).","Answer",{"name":59,"@type":54,"acceptedAnswer":60},"How do you choose which side of the line to shade for an inequality?",{"text":61,"@type":57},"Pick the unwanted side, then test uncertainty by substituting a point not on the line into the inequality to see whether it satisfies the inequality on that side.",{"name":63,"@type":54,"acceptedAnswer":64},"If a question asks for the maximum or minimum in a shaded region, how do you find it?",{"text":65,"@type":57},"For maximum, choose the coordinate furthest to the top-right (largest x and y). For minimum, choose the coordinate furthest to the bottom-left (smallest x and y).","https://schema.org",{"og:url":32,"og:type":68,"og:title":10,"og:site_name":40,"og:description":12},"article",{"robots":70,"canonical":32},"index,follow",{"doc_id":72,"site_id":7},207092,1788597902,{"code":4,"msg":75,"data":76},"success",[77,81,85,88,93,98,103,108,113,116,120],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":78,"show_sort_weight":79,"slug":80},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":82,"show_sort_weight":83,"slug":84},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":86,"slug":87},70,"exam",{"id":89,"doc_module":4,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},5,"Comic",60,"comic",{"id":94,"doc_module":4,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},6,"Technology",50,"technology",{"id":99,"doc_module":4,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},7,"Healthcare",40,"healthcare",{"id":104,"doc_module":4,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},8,"Research & Report",30,"research-report",{"id":109,"doc_module":4,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},9,"Religion & Spirituality",20,"religion-spirituality",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":114,"show_sort_weight":111,"slug":115},"World Cup","world-cup",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":118,"show_sort_weight":117,"slug":119},10,"Lifestyle","lifestyle",{"id":121,"doc_module":4,"doc_module_name":25,"category_name":122,"show_sort_weight":89,"slug":123},19,"General","general",{"code":4,"msg":75,"data":125},{"doc_id":72,"user_id":126,"nickname":37,"user_avatar":127,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":109,"language":133,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":134,"faqs":135,"seo_title":136,"seo_description":12,"update_tm":73,"read_time":137},962075114765,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Head to www.savemyexams. com for more awesome resources  \n OCR GCSE Maths  \nGraphing Inequalities  \nContents  \n Graphing Inequalities  \nPage 1 of 9  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nGraphing Inequalities  \nFinding Regions using Inequalities  \nHow do we draw inequalities on a graph?  \n First, see Straight Line Graphs (y = mx + c)  \nTo graph an inequality;  \n􀂋 . DRAW the line (as if using “=”) for each inequality  \n Use a solid line for ≤ or ≥ (to indicate the line is included)  \n Use dotted line for \u003C or > (to indicate the line is not included)  \n􀂌 . DECIDE which side of line is wanted.  \n Below line if \"y ≤ . . . \" or \"y \u003C . . . \"  \n Above line if \"y ≥ . . . \" or \"y > . . . \"  \n Use a point that 's not on the line as a test if unsure; substitute its x andy value into the inequality to examine whether the inequality holds true on that side of the line  \n􀂍 . Shade UNWANTED side of each line (unless the question says otherwise)  \n This is because it is easier, with pen/ pencil/ paper at least, to see which region has not been shaded than it isto look for a region that has been shaded 2−3 times or more  \n (Graphing software often shades the area that is required but this is easily overcome by reversing the inequality sign)  \nPage 2 of 9  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n Worked example  \nOn the axes given below, show the region that satis|es the three inequalities;  \n3x + 2y ≥ 12 y \u003C2x x \u003C3  \nLabel the region R.  \nFirst draw the three straight lines, ,  and, using your knowledge of  \nStraight Line Graphs (y = mx + c) . You may wish to rearrangeto the form  \n |rst:  \nThe linetakes a solid line because of the \" ≥ \" while the linesandtake dotted lines because of the \" \u003C \"  \nPage 3 of 9  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nNow we need to shade the unwanted regions  \nFor(or) , the unwanted region is below the line. We can check this with the point (0 , 0);  \n is false therefore (0 , 0) does lie in the unwanted region for  \nFor, the unwanted region is above the line. If unsure, check with another point, for example (1 , 0)  \nis true, so (1 , 0) lies in the wanted (i. e. unshaded) region for  \nFor, shade the unwanted region to the right of . If unsure, check with a point  \nPage 4 of 9  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nFinally, don 't forget to label the region R  \nPage 5 of 9  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nInterpreting Graphical Inequalities  \nHow do we interpret inequalities on a graph?  \n First, see Straight Line Graphs (y = mx + c)  \nTo interpret inequalities/ to |nd a region de|ned by inequalities;  \n􀂋 . Write down the EQUATION of each line on the graph 􀂌 . REMEMBER that lines are drawn with:  \n A solid line for ≤ or ≥ (to indicate line included in region)  \n A dotted line for \u003C or > (to indicate line not included)  \n􀂍 . REPLACE = sign with:  \n ≤ or \u003C if shading below line  \n ≥ or > if shading above line  \n (Use a point to test if not sure)  \n If the question asks you to |nd the maximum in a region, |nd the coordinate furthest to the top-right (largest values of x andy)  \n If the question asks you to |nd the minimum in a region, |nd the coordinate furthest to the bottom-left (smallest values of x andy)  \nPage 6 of 9  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n Worked example  \nWrite down the three inequalities which de|ne the","cbCaibV1aMC9AB4V","https://ap.wps.com/l/cbCaibV1aMC9AB4V","pdf",1771371,"English","# Graphing Inequalities\n## Finding Regions using Inequalities\n## Worked example\n# Interpreting Graphical Inequalities\n## How do we interpret inequalities on a graph?\n## Worked example","[{\"question\":\"How do you decide whether a boundary line should be solid or dotted when graphing an inequality?\",\"answer\":\"Use a solid line for ≤ or ≥ (the line is included) and a dotted line for \\u003c or \\u003e (the line is not included).\"},{\"question\":\"How do you choose which side of the line to shade for an inequality?\",\"answer\":\"Pick the unwanted side, then test uncertainty by substituting a point not on the line into the inequality to see whether it satisfies the inequality on that side.\"},{\"question\":\"If a question asks for the maximum or minimum in a shaded region, how do you find it?\",\"answer\":\"For maximum, choose the coordinate furthest to the top-right (largest x and y). For minimum, choose the coordinate furthest to the bottom-left (smallest x and y).\"}]","Graphing Inequalities - Finding Regions using Inequalities | PDF",23]