[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207797-en":3,"doc-seo-207797-105":30,"detail-sidebar-cat-0-en-105":93},{"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},207797,1374404730887,"Pentious","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",4,"Exam","Equations: Letters on Both Sides","This document provides a comprehensive set of practice problems on solving linear equations with variables on both sides, suitable for exam preparation. It includes multiple-choice questions, equations to solve, and word problems that require setting up and solving equations. The exercises cover a range of difficulties, from basic algebraic manipulation to more complex scenarios involving geometric shapes and function machines. The document is sourced from Corbettmaths, a reputable educational resource for mathematics. The practice problems are designed to reinforce understanding of algebraic concepts, including variable isolation, equation balancing, and problem-solving strategies. Specific questions address the interpretation of diagrams, such as rectangles and isosceles triangles, to form algebraic expressions and equations. The document also includes a section for identifying mistakes in solved problems, promoting critical thinking and error analysis in mathematics. The comprehensive nature of the questions ensures that students can practice and master the skills needed to solve equations with letters on both sides, a fundamental concept in algebra. The document emphasizes practical application of algebraic principles through various question types.","Equations: Letters on Both Sides Video 113 on [www.corbettmaths.com](www.corbettmaths.com)  \nClick here  \nQuestion 1: Solve the following equations  \n(a)    (b)    (c)     \n(d)    (e)  ~~ ~~    (f)  ~~ ~~   \n(g)   (h)  ~~ ~~  (i)  ~~ ~~   ~~ ~~   \n(j)   ~~ ~~  (k)  ~~ ~~   ~~ ~~  (l)    ~~ ~~   \n(m)  ~~ ~~   ~~ ~~  (n)    ~~ ~~  (o)  ~~ ~~  ~~ ~~   \n(p)  ~~ ~~   ~~ ~~  (q)    (r)   \nQuestion 2: Solve the following equations  \n(a)   (b)   (c)    ~~ ~~   \n(d)   ~~ ~~  (e)    (f)      \n(g)      (h)      (i)         \nQuestion 3: Solve the following equations  \n(a)    (b)   (c)     \n(d)      (e)        (f)       \n(g)    ~~ ~~  ~~ ~~  (h) ~~ ~~  ~~ ~~   (i) ~~ ~~  ~~ ~~  ~~ ~~   \n© CORBETTMATHS 2018  \nEquations: Letters on Both Sides Video 113 on [www.corbettmaths.com](www.corbettmaths.com)  \nQuestion 4: Solve the following equations  \n(a)    (b)  ~~ ~~   (c)   \n(d)  ~~ ~~   ~~ ~~  (e)  ~~ ~~    (f)  ~~ ~~   \n(g)      \n(h)  ~~ ~~  ~~ ~~  ~~ ~~     \nApply  \nQuestion 1: Shown is a rectangle  \n(a) Explain why 9x + 12 = 4x + 47  \n(b) Find x  \nQuestion 2: Shown is an isosceles triangle  \n(a) Explain why 4x + 15 = 33 − 2x  \n(b) Find x  \n(c) Find the perimeter of the isosceles triangle  \nQuestion 3: Explain why 8x + 3 = 2(4x + 1) has no solution.  \nQuestion 4: (a) Find the value of x  \n(b) Find the value of y  \n* The mass of the balances are very small, so may be ignored  \n© CORBETTMATHS 2018  \nEquations: Letters on Both Sides Video 113 on [www.corbettmaths.com](www.corbettmaths.com)  \nQuestion 5: Shown below is a function machine.  \nThe input and output have the same value.  \n(a) Write an equation in terms of x.  \n(b) Solve the equation to Wind the value of x.  \nQuestion 6: Toby has completed his homework.  \nCan you spot any mistakes?  \nAnswers  \nClick here  \n© CORBETTMATHS 2018","cbCaivUwKCmmkg53","https://ap.wps.com/l/cbCaivUwKCmmkg53","pdf",543331,1,3,"English","en",105,"# Question 1\n## Solve the following equations\n# Question 2\n## Solve the following equations\n# Question 3\n## Solve the following equations\n# Question 4\n## Solve the following equations\n# Apply\n## Question 1\n### Shown is a rectangle\n## Question 2\n### Shown is an isosceles triangle\n## Question 3\n### Explain why 8x + 3 = 2(4x + 1) has no solution.\n## Question 4\n### (a) Find the value of x\n### (b) Find the value of y\n# Question 5\n## Shown below is a function machine.\n## Question 6\n## Toby has completed his homework.","[{\"question\":\"What is the main topic of this document?\",\"answer\":\"The main topic of this document is solving linear equations with variables on both sides of the equation.\"},{\"question\":\"What types of problems are included in this practice set?\",\"answer\":\"This practice set includes solving basic linear equations, word problems involving geometric shapes, and problems related to function machines, as well as identifying errors in solved problems.\"},{\"question\":\"What is the purpose of the balance scale image in Question 4?\",\"answer\":\"The balance scale image in Question 4 is used to represent an equation where the masses on both sides must be equal, helping to visualize the concept of balancing equations.\"},{\"question\":\"What is the significance of the 'Apply' section?\",\"answer\":\"The 'Apply' section presents word problems that require students to translate real-world scenarios, such as those involving geometric shapes, into algebraic equations before solving them.\"}]","Equations: Letters on Both Sides | 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