[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-487026-105":3,"detail-sidebar-cat-0-en-105":85,"doc-detail-487026-en":134},{"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":78,"head_meta":80,"extra_data":82,"updated_unix":84},105,"en","solving-linear-equations-learning-sheet","Solving Linear Equations - Learning Sheet","","Solving Linear Equations explains how to find the value of a variable that makes a linear equation true. It introduces equality properties—addition, subtraction, multiplication, and division—and shows how they justify isolating the variable. The material also covers clearing fractions and decimals to simplify solving. A step-by-step method guides simplifying, collecting like terms, making the coefficient 1, and checking solutions, including identity, contradiction, and conditional cases, plus worked examples and practice problems.",{"@graph":14,"@context":77},[15,34,56],{"@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/solving-linear-equations-learning-sheet/487026/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/solving-linear-equations-learning-sheet/487026.png","ImageObject",300,407,{"name":42,"@type":43},"Mary Man","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69,73],{"name":60,"@type":61,"acceptedAnswer":62},"What is the goal of solving a linear equation?","Question",{"text":63,"@type":64},"The goal is to find the variable value that makes the equation statement true.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which properties of equality are used to isolate the variable?",{"text":68,"@type":64},"Addition and subtraction properties collect terms by moving expressions to opposite sides. Multiplication and division properties scale both sides to make the variable coefficient equal to 1.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you clear fractions or decimals when solving equations?",{"text":72,"@type":64},"Clear fractions by multiplying both sides by the LCD of the denominators. Clear decimals by multiplying both sides by the lowest power of 10 that makes all decimals whole numbers.",{"name":74,"@type":61,"acceptedAnswer":75},"How can you tell an identity, contradiction, or conditional equation?",{"text":76,"@type":64},"If eliminating variables reveals a true statement, it is an identity (all real numbers). If it reveals a false statement, it is a contradiction (no solution). Otherwise, it is conditional (one solution).","https://schema.org",{"og:url":32,"og:type":79,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":81,"canonical":32},"index,follow",{"doc_id":83,"site_id":7},487026,1792832882,{"code":4,"msg":86,"data":87},"success",[88,92,96,99,103,108,113,118,123,126,130],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":97,"slug":98},70,"exam",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},"Comic",60,"comic",{"id":104,"doc_module":4,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},6,"Technology",50,"technology",{"id":109,"doc_module":4,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},7,"Healthcare",40,"healthcare",{"id":114,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},8,"Research & Report",30,"research-report",{"id":119,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},9,"Religion & Spirituality",20,"religion-spirituality",{"id":121,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":121,"slug":125},"World Cup","world-cup",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":127,"slug":129},10,"Lifestyle","lifestyle",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":132,"show_sort_weight":55,"slug":133},19,"General","general",{"code":4,"msg":86,"data":135},{"doc_id":83,"user_id":136,"nickname":42,"user_avatar":137,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":138,"file_id":139,"file_url":140,"file_type":141,"file_size":142,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":143,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":144,"faqs":145,"seo_title":146,"seo_description":12,"update_tm":147,"read_time":127,"preview_page_count":4},7421720224475,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","SOLVING LINEAR EQUATIONS  \nGoal: The goal of solving a linear equation is to find the value of the variable that will make the statement (equation) true.  \nMethod: Perform operations to both sides of the equation in order to isolate the variable.  \nAddition and Subtraction Properties of Equality:  \nLet 􀀁, 􀀂 , and 􀀃 represent algebraic expressions.  \n1. Addition property of equality:  \nIf 􀀁 􀀄 􀀂 ,  \nthen 􀀁 􀀅 􀀃 􀀄 􀀂 􀀅 􀀃  \n2. Subtraction property of equality:  \nIf 􀀁 􀀄 􀀂 ,  \nthen 􀀁 􀀆 􀀃 􀀄 􀀂 􀀆 􀀃  \nMultiplication and Division Properties of Equality:  \nLet 􀀁, 􀀂 , and 􀀃 represent algebraic expressions.  \n1. Multiplication property of equality:  \nIf 􀀁 􀀄 􀀂 ,  \nthen 􀀁􀀃 􀀄 􀀂􀀃  \n2. Division property of equality:  \nIf 􀀁 􀀄 􀀂 ,  \nthen 􀀇􀀈 􀀄 􀀉􀀈 (provided 􀀃 􀀊 0)  \nClearing Fractions or Decimals in an Equation:  \nWhen solving an equation with fractions or decimals, there is an option of clearing the fractions or decimals in order to create a simpler equation involving whole numbers.  \n1. To clear fractions, multiply both sides of the equation (distributing to all terms) by the LCD of all the fractions.  \n2. To clear decimals, multiply both sides of the equation (distributing to all terms) by the lowest power of 10 that will make all decimals whole numbers.  \nSteps for Solving a Linear Equation in One Variable:  \n1. Simplify both sides of the equation.  \n2. Use the addition or subtraction properties of equality to collect the variable terms on one side of the equation and the constant terms on the other.  \n3. Use the multiplication or division properties of equality to make the coefficient of the variable term equal to 1.  \n4. Check your answer by substituting your solution into the original equation.  \nNote: If when solving an equation, the variables are eliminated to reveal a true statement such as,􀀆13 􀀄 􀀆13 , then the solution is all real numbers. This type of equation is called an identity. On the other hand, if the variables are eliminated to reveal a false statement such as, 􀀆7 􀀄 3 , then there is no solution. This type of equation is called a contradiction. All other linear equations which have only one solution are called conditional.  \nExamples:  \nA. 􀀏 􀀅 5 􀀄 􀀆2  \n􀀆5 􀀆 5  \n􀀏 􀀄 􀀆7  \nB. 􀀏 􀀆 3 􀀄 7  \n 􀀅3 􀀅3   \n􀀏 􀀄 10  \nCheck:  \n􀀒􀀆7􀀓 􀀅 5 􀀄 􀀆2  \n􀀆2 􀀄 􀀆2 (Solution Checks) Check:  \n10 􀀆 3 􀀄 7  \n7 􀀄 7 (Solution Checks)  \nC. 3􀀏 􀀄 24  \n3􀀏 24  \n~~ ~~ 􀀄 ~~ ~~  \n3 3  \n􀀏 􀀄 8  \nD. 􀀆7􀀏 􀀄 28  \n􀀆7􀀏 28 ~~ ~~ 􀀄 ~~ ~~  \n􀀆7 􀀆7  \n􀀏 􀀄 􀀆4  \nE. 􀀗􀀘 􀀏 􀀄 􀀆4 􀀘􀀗 · 􀀗􀀘 􀀏 􀀄 􀀚􀀜􀀛 · 􀀘􀀗 (Multiply by the reciprocal)  \n􀀏 􀀄 􀀆6 F. 􀀠􀀚􀀡 􀀄 2  \n􀀆15 · 5 􀀄 2􀀒􀀆5􀀓  \n􀀢 􀀄 􀀆10 Identity Example:  \nG. 2􀀏 􀀅 6 􀀄 3􀀒􀀏 􀀅 2􀀓 􀀆 􀀏 2􀀏 􀀅 6 􀀄 3􀀏 􀀅 6 􀀆 􀀏 2􀀏 􀀅 6 􀀄 2􀀏 􀀅 6  \n􀀆2􀀏 􀀆 2􀀏  \n6 􀀄 6 True Statement Solution: all real numbers  \nI. 10 􀀆 5􀀏 􀀄 3􀀒􀀏 􀀆 4􀀓 􀀆 2􀀒􀀏 􀀅 7􀀓  \n10 􀀆 5􀀏 􀀄 3􀀏 􀀆 12 􀀆 2􀀏 􀀆 14  \n10 􀀆 5􀀏 􀀄 􀀏 􀀆 26  \n 􀀆􀀏 􀀆 􀀏   \n10 􀀆 6􀀏 􀀄 􀀆26  \n􀀆10 􀀆 10  \n􀀆6􀀏 􀀄 􀀆36  \n􀀚􀀣􀀤 􀀚􀀘􀀣  \n~~ ~~ 􀀄 ~~ ~~  \n􀀚􀀣 􀀚􀀣  \n􀀏 􀀄 6  \nJ. 􀀤~~ ~~􀀗 􀀆 􀀤~~ ~~􀀛 􀀄 2 (LCD is 10)  \n10 􀀞􀀏~~ ~~~~ ~~2 􀀆 􀀏~~ ~~~~ ~~4􀀟 􀀄 2 􀀒10􀀓  \n10 􀀒􀀏 􀀆 2􀀓 10 􀀒􀀏 􀀆 4􀀓  \n · ~~ ~~ 􀀆  · ~~ ~~ 􀀄 20  \n1 5 1 2 2􀀒􀀏 􀀆 2􀀓 􀀆 5􀀒􀀏 􀀆 4􀀓 􀀄 20  \n2􀀏 􀀆 4 􀀆 5􀀏 􀀅 20 􀀄 20  \n􀀆3􀀏 􀀅 16 􀀄 20  \n􀀆16 􀀆 16  \n􀀚􀀘􀀤  \n􀀚􀀘  \n􀀄  \n 􀀛   \n􀀚􀀘  \n􀀛  \nCheck:  \n3􀀒8􀀓 􀀄 24  \n24 􀀄 24 (Solution Checks)  \nCheck:  \n􀀆7􀀒􀀆4􀀓 􀀄 28  \n28 􀀄 28 (Solution Checks)  \nCheck:  \n23 􀀞~~ ~~􀀆16􀀟 􀀄 􀀆4  \n􀀆4 􀀄 􀀆4 (Solution Checks)  \nCheck:  \n􀀆10  \n􀀆5  \n􀀄 2  \n2 􀀄 2 (Solution Checks)  \nContradiction Example:  \nH. 5􀀏 􀀆 3 􀀄 4􀀒􀀏 􀀅 2􀀓 􀀅 􀀏 5􀀏 􀀆 3 􀀄 4􀀏 􀀅 8 􀀅 􀀏 5􀀏 􀀆 3 􀀄 5􀀏 􀀅 8  \n􀀆5􀀏 􀀆 5􀀏  \n􀀆3 􀀄 8 False Statement No Solution  \nCheck:  \n10 􀀆 5􀀒6􀀓 􀀄 3􀀒6 􀀆 4􀀓 􀀆 2􀀒6 􀀅 7􀀓  \n10 􀀆 30 􀀄 3􀀒2􀀓 􀀆 2􀀒13􀀓  \n􀀆20 􀀄 6 􀀆 26  \n􀀆20 􀀄 􀀆20 (Solution Checks)  \nK. 0. 05􀀏 􀀅 0 . 25 􀀄 0 .2 100􀀒0 . 05􀀏 􀀅 0 . 25􀀓 􀀄 0 . 2􀀒100􀀓 5􀀏 􀀅 25 􀀄 20  \n 􀀆25 􀀆 25  \n􀀡􀀤 􀀚􀀡  \n~~ ~~ 􀀄 ~~ ~~  \n􀀡 􀀡  \n􀀏 􀀄 􀀆1 Check:  \n0.05􀀒􀀆1􀀓 􀀅 0 . 25 􀀄 0 .2  \n􀀆0.05 􀀅 0.25 􀀄 0.2  \n0. 2 􀀄 0 .2 (Solution Checks)  \n􀀏 􀀄 􀀆 􀀘  \nLINEAR EQUATIONS PRACTICE  \n1. 4􀀏 􀀄 4  \n2. 􀀏 􀀅 6 􀀄 􀀆7  \n3. 􀀏 􀀆 4 􀀄 7  \n4. 􀀤􀀘 􀀄 􀀆9  \n5. 2􀀏 􀀅 4 􀀄 8  \n6. 14 􀀄 3 􀀅 2􀀏  \n7. 8􀀏 􀀆 3 􀀄 􀀆19  \n8. 6 􀀆 􀀏 􀀄 9  \n9. 􀀆􀀏 􀀄 􀀆12  \n10. 3􀀒􀀏 􀀆 2􀀓 􀀄 6  \n11. 􀀆3􀀒2􀀏 􀀆","cbCaifxGTs41ySXJ","https://ap.wps.com/l/cbCaifxGTs41ySXJ","pdf",78373,"English","# Goal and Method\n## Properties of Equality (Addition/Subtraction)\n## Properties of Equality (Multiplication/Division)\n## Clearing Fractions and Decimals\n# Steps to Solve a One-Variable Linear Equation\n## Checking Solutions\n# Identity, Contradiction, and Conditional Equations\n# Examples and Practice","[{\"question\":\"What is the goal of solving a linear equation?\",\"answer\":\"The goal is to find the variable value that makes the equation statement true.\"},{\"question\":\"Which properties of equality are used to isolate the variable?\",\"answer\":\"Addition and subtraction properties collect terms by moving expressions to opposite sides. Multiplication and division properties scale both sides to make the variable coefficient equal to 1.\"},{\"question\":\"How do you clear fractions or decimals when solving equations?\",\"answer\":\"Clear fractions by multiplying both sides by the LCD of the denominators. Clear decimals by multiplying both sides by the lowest power of 10 that makes all decimals whole numbers.\"},{\"question\":\"How can you tell an identity, contradiction, or conditional equation?\",\"answer\":\"If eliminating variables reveals a true statement, it is an identity (all real numbers). If it reveals a false statement, it is a contradiction (no solution). Otherwise, it is conditional (one solution).\"}]","Solving Linear Equations - Learning Sheet | PDF",1790807668]