[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207520-en":3,"doc-seo-207520-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207520,1099514067438,"River Wang","https://ap-avatar.wpscdn.com/avatar/100002539ee87300030?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780474512215547542",4,"Exam","AQA GCSE Further Maths - Solving Inequalities - Linear Inequalities","Revision notes for AQA GCSE Further Maths focused on solving inequalities, especially linear and double inequalities. Covers definitions of linear inequalities and which expressions qualify, key rules for solving them by analogy with linear equations, and the requirement to keep inequality signs while reversing direction when multiplying or dividing by a negative number. Explains how to represent solutions using number lines and set notation, and includes worked examples with number-line and set-notation answers.","Head to www.savemyexams. com for more awesome resources  \n AQA GCSE Further Maths  \nSolving Inequalities  \nContents  \n Linear Inequalities  Quadratic Inequalities  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nLinear Inequalities  \nLinear Inequalities What is a linear inequality?  \n An inequality tells you that one expression is greater than (“ >”) or less than (“ \u003C”) another  \n “⩾” means “greater than or equal to”  \n “⩽” means “less than or equal to”  \n A linear inequality only has constant terms (numbers with no letters) and terms in x (and/or ay); but nox2 terms or terms with higher powers of x  \n For example, 3x2 > 12 is not a linear inequality (it is a quadratic inequality)  \n For example, 3x + 4 ⩾ 7 would be read “3× + 4 is greater than or equal to 7”.  \nHow do I solve linear inequalities?  \n Solving linear inequalities is just like Solving Linear Equations  \n Follow the same rules, but keep the inequality sign throughout  \n If you change the inequality sign to an equals sign you are changing the meaning of the problem  \n When you multiply or divide both sides by a negative number, you must }ip the sign of the inequality  \n e. g. 1 \u003C 2 → [times both sides by (–1)] → –1 > –2 (sign }ips)  \n Never multiply or divide by a variable (x) as this could be positive or negative  \n The safest way to rearrange is simply to add & subtract to move all the terms onto one side  \n You also need to know how to use Number Lines, Set Notation and deal with “Double” Inequalities  \nHow do I represent linear inequalities on a number line?  \n Inequalities such as x \u003C a and x > a can be represented on a normal number line using an open circle and an arrow  \n For \u003C , the arrow points to the left of a  \n For > , the arrow points to the right of a  \n Inequalities such as x ≤ a and x ≥ a can be represented on a normal number line using a solid circle and an arrow  \n For ≤ , the arrow points to the left of a  \n For ≥ , the arrow points to the right of a  \n Inequalities such as a \u003C x \u003C band a ≤ x ≤ b can be represented on a normal number line using two circles at a and b and a line between them  \n For \u003C or > use an open circle  \n For ≤ or ≥ , use a solid circle  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \n Disjoint inequalities such as \" x \u003C a or x > b \" can be represented with two circles at a and b, anarrowed line pointing left from a and an arrowed line pointing right from b , and a blank space between a and b  \nHow do I represent linear inequalities using set notation?  \n We use curly brackets and a colon in set notation. {x: . . . } means \"x is in the set ... \"  \n For example; if x is greater than 3 , then in set notation, {x: x > 3}  \n However, if x is between two values, then the two end values must be written in separate sets, using the intersection symbol, ∩  \n For example, if x is greater than 3 and less than or equal to 5 , then in set notation,{x: x >3} ∩ {x: x ≤5}  \n Similarly, if x is less than one value or greater than another (disjoint) , then the two end values must be written in separate sets using the union symbol, ∪  \n For example, if x is less than 3 or greater than or equal to 5 , then in set notation,{x: x \u003C3} ∪ {x: x ≥5}  \nHow do I solve double inequalities?  \n Inequalities such as a \u003C 2x \u003C b can be solved by doing the same thing to all three parts of the inequality  \n Use the same rules as solving linear inequalities  \n Exam Tip  \n Do not change the inequality sign to an equals when solving linear inequalities, you will lose marks in an exam for doing this.  \n Remember to reverse the direction of the inequality sign when multiplying or dividing by a negative number!  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome res","cbCaikeQCjORRvMl","https://ap.wps.com/l/cbCaikeQCjORRvMl","pdf",1307234,1,8,"English","en",105,"# Contents\n## Linear Inequalities\n## Quadratic Inequalities\n## Worked example - Double inequalities\n## Worked example - Single linear inequality","[{\"question\":\"What makes an inequality a linear inequality in GCSE Further Maths?\",\"answer\":\"A linear inequality must have only constant terms and terms in x (and/or ay) with no x squared or higher power terms. If an expression includes x^2 terms, it is not linear and becomes quadratic.\"},{\"question\":\"How do you solve a linear inequality correctly?\",\"answer\":\"Solve it like a linear equation, but keep the inequality sign throughout. When multiplying or dividing both sides by a negative number, reverse the inequality direction. Avoid multiplying or dividing by a variable.\"},{\"question\":\"How can solutions to linear inequalities be represented on a number line and using set notation?\",\"answer\":\"Use an open circle for \\u003c or \\u003e and a solid circle for ≤ or ≥, with arrows showing direction. For set notation, write {x: ...} using curly brackets and a colon, combine ranges with intersection (∩) for between-values, and use union (∪) for disjoint ranges.\"}]","AQA GCSE Further Maths - Solving Inequalities - Linear Inequalities | PDF",1788599879,20,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"aqa-gcse-further-maths-solving-inequalities-linear-inequalities","",{"@graph":36,"@context":84},[37,53,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/aqa-gcse-further-maths-solving-inequalities-linear-inequalities/207520/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What makes an inequality a linear inequality in GCSE Further Maths?","Question",{"text":74,"@type":75},"A linear inequality must have only constant terms and terms in x (and/or ay) with no x squared or higher power terms. If an expression includes x^2 terms, it is not linear and becomes quadratic.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How do you solve a linear inequality correctly?",{"text":79,"@type":75},"Solve it like a linear equation, but keep the inequality sign throughout. When multiplying or dividing both sides by a negative number, reverse the inequality direction. Avoid multiplying or dividing by a variable.",{"name":81,"@type":72,"acceptedAnswer":82},"How can solutions to linear inequalities be represented on a number line and using set notation?",{"text":83,"@type":75},"Use an open circle for \u003C or > and a solid circle for ≤ or ≥, with arrows showing direction. For set notation, write {x: ...} using curly brackets and a colon, combine ranges with intersection (∩) for between-values, and use union (∪) for disjoint ranges.","https://schema.org",{"og:url":52,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,103,108,113,118,122,126,129,133],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":101,"slug":102},70,"exam",{"id":104,"doc_module":4,"doc_module_name":46,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":109,"doc_module":4,"doc_module_name":46,"category_name":110,"show_sort_weight":111,"slug":112},6,"Technology",50,"technology",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":119,"show_sort_weight":120,"slug":121},"Research & Report",30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":29,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":29,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":29,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":104,"slug":136},19,"General","general"]