[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-465954-105":59,"doc-detail-465954-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","expressing-inequalities-on-a-number-line","Expressing Inequalities on a Number Line","","Use the number line to represent and interpret inequalities involving x. The worksheet provides example inequality markers and multiple items showing x compared to specific threshold values using ≤, >, \u003C, and ≥. For each problem, the correct region is identified by selecting all points on the number line that satisfy the given inequality direction and boundary condition. Topics include choosing values less than, greater than, and including or excluding the endpoint.",{"@graph":69,"@context":122},[70,84,105],{"@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/expressing-inequalities-on-a-number-line/465954/",{"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/expressing-inequalities-on-a-number-line/465954.png","ImageObject",300,407,{"name":92,"@type":93},"Aria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you express an inequality on a number line?","Question",{"text":112,"@type":113},"Locate the boundary value on the number line and shade the side that matches the inequality direction for x. Use the inequality symbol to decide whether the boundary point is included or not.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does x ≤ (less than or equal to) mean on a number line?",{"text":117,"@type":113},"It includes the boundary point. Shade all points at or below the given number, using a closed endpoint at the boundary.",{"name":119,"@type":110,"acceptedAnswer":120},"What does x \u003C (strictly less than) mean on a number line?",{"text":121,"@type":113},"It excludes the boundary point. Shade all points strictly below the given number, using an open endpoint at the boundary.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},465954,1790770320,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":39},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","Use the numberline to express the inequality.  \nEx) -150 -145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90  \nX ≤ -125               \n1) -104 -103 -102 -101 -100 -99 -98 -97 -96 -95 -94 -93 -92 -91 X > -98   \n2) -95 -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 X ≤ -60   \n3) 20 25 30 35 40 45 50 55 60 65 70 X \u003C 45   \n4) -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 X > -7   \n5) 100 105 110 115 120 125 130 135 140 145 150 155 160 165 X ≤ 130   \n6) -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 X ≤ -40   \n7) -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 X > -80   \n8) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 X > 60   \n9) 85 90 95 100 105 110 115 120 125 130 135 140 145 150 X ≥ 115   \n10) -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 X ≥ -20   \n1-10  90  80  70  60  50  40  30  20  10  0   \n [Math ](Math  www.CommonCoreSheets.com 2)[ www.CommonCoreSheets.com](Math  www.CommonCoreSheets.com 2)[ 2](Math  www.CommonCoreSheets.com 2) ~~                   ~~  \nUse the numberline to express the inequality.  \nEx) -150 -145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90  \nX ≤ -125   \nX  \n1) -104 -103 -102 -101 -100 -99 -98 -97 -96 -95 -94 -93 -92 -91 X > -98 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~~~ ~~  \n2) -95 -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 X ≤ -60   \nX  \n3) 20 25 30 35 40 45 50 55 60 65 70 X \u003C 45 ~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~  \n4) -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 X > -7 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n5) 100 105 110 115 120 125 130 135 140 145 150 155 160 165 X ≤ 130   \nX  \n6) -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 X ≤ -40   \nX  \n7) -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 X > -80 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~  \n8) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 X > 60 ~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~X~~ ~~~~ ~~~~ ~~~~ ~~  \n9) 85 90 95 100 105 110 115 120 125 130 135 140 145 150 X ≥ 115   \nX  \n10) -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 X ≥ -20   \nX  \n1-10  90  80  70  60  50  40  30  20  10  0   \n [Math ](Math  www.CommonCoreSheets.com 2)[ www.CommonCoreSheets.com](Math  www.CommonCoreSheets.com 2)[ 2](Math  www.CommonCoreSheets.com 2) ~~                   ~~  \nUse the numberline to express the inequality.  \nEx) X ≤ -125  \n-150 -145 -140 -135 -130 -125 -120 -115 -110 -105 -100 -95 -90  \n1) X > -98  \n-104 -103 -102 -101 -100 -99 -98 -97 -96 -95 -94 -93 -92 -91  \n2) X ≤ -60  \n-95 -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35  \n3) X \u003C 45  \n20 25 30 35 40 45 50 55 60 65 70  \n4) X > -7  \n-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1  \n5) X ≤ 130  \n100 105 110 115 120 125 130 135 140 145 150 155 160 165  \n6) X ≤ -40  \n-75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10  \n7) X > -80  \n-150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20","cbCaitjIiG4h7A6e","https://ap.wps.com/l/cbCaitjIiG4h7A6e","pdf",64174,"English","# Express the inequality on a number line\n## Examples and x ≤ / x > / x \u003C / x ≥ problems","[{\"question\":\"How do you express an inequality on a number line?\",\"answer\":\"Locate the boundary value on the number line and shade the side that matches the inequality direction for x. Use the inequality symbol to decide whether the boundary point is included or not.\"},{\"question\":\"What does x ≤ (less than or equal to) mean on a number line?\",\"answer\":\"It includes the boundary point. Shade all points at or below the given number, using a closed endpoint at the boundary.\"},{\"question\":\"What does x \\u003c (strictly less than) mean on a number line?\",\"answer\":\"It excludes the boundary point. Shade all points strictly below the given number, using an open endpoint at the boundary.\"}]","Expressing Inequalities on a Number Line | PDF"]