[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267363-105":59,"doc-detail-267363-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","express-operations1-answer-key","Express Operations1 Answer Key","","Answer key provides step-by-step solutions for a set of algebra and arithmetic exercises. The material covers simplifying expressions, solving linear equations and systems, using distribution and the distributive law, factoring using number properties, working with consecutive even numbers, applying substitution to age and money word problems, and interpreting revenue and pricing changes. It also includes guidance for handling large exponents with equivalent common formats.",{"@graph":69,"@context":123},[70,84,106],{"@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/express-operations1-answer-key/267363/",{"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/express-operations1-answer-key/267363.png","ImageObject",300,407,{"name":92,"@type":93},"Blaney","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",18,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics are covered in the answer key?","Question",{"text":113,"@type":114},"The key covers simplifying algebraic expressions, solving linear equations and systems, applying distribution, and working through word problems involving age, money, and revenue.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are linear equations like 6x-14=40 solved?",{"text":118,"@type":114},"The steps shown include adding or subtracting constants to isolate the term with x, then dividing to get the value of x.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the document suggest dealing with comparing extremely large numbers?",{"text":122,"@type":114},"It explains that calculators may overflow for expressions like 99100, so rewriting terms into a common format allows straightforward comparison.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},267363,1789417684,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":24},1236954677761,"https://us-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","No Calculator  \n1.1(1-(1-(1-2))-(1-(1-(1-3))Parentheses:(1-(1-(-1))-(1-(1-(-2)))Next parentheses:(1-(2))-(1-(3)Next parentheses:(-1)-(-2)Subtract:-1+2=1  \n2.9/2 or 4.5  \n6x-14=40  \nAdd 14:  \n6x=54  \nDivide by 6:  \nx=9  \n3.22 Letnbe the least of these numbers.The sum offour consecutive even numbers is thereforen+(n+2)+(n+4)+(n+6)=76.  \nSimplify:4n+12=76Subtract 12:4n=64Divide by 4:n=16Therefore the largest of these numbers is 16+6=22  \n4.28Multiply by4:10x+12=28  \n5.7/6 or 1.16 or 1.17  \nx-7=-5xSubtract x:  \n-7=-6xDivide by-6:  \n6.0  \n5d+12=24Subtract 24:5d-12=0  \n7.5Subtract y²:Multiply by-5/3:Take square root:  \ny=0Add 5:y+5=5  \n8.C Ifxy=36andxandyare integers,thenxandyareboth factors of 36.In order to minimize the value ofx-y,we must find the greatest separation between xandy.Thegreatest separation between a factor pair is1-36=-35.  \n9.A We should regard this as a “conversion”prob-lem fromm days into a corresponding number of dollars.  \n# EXERCISE SET 1 ANSWER KEY\n\n10.B Original expression:  \n5x(2x×3)-5x²  \nParentheses:  \n5x(6x)-5x²  \nMultiply:  \n30x²-5x²  \nSubtract:  \n25x²  \nRemember:The Law of Distribution does not apply inthe first step,because the grouped expression doesn'tinclude addition or subtraction.  \n11.D The simplest approach is perhaps to choosesimple values for x and y,like 2 and 3,and see whichoperator yields a true equation.Since(2÷3)×(3÷2)=1,the answer is(D).  \nCalculator  \n12.45  \na-b=4  \na+b=14  \nAdd equations:  \n2a=18  \nDivide by2:  \na=9  \nSubstitute a=9:  \n9+b=14  \nSubtract 9:  \nb=5  \nEvaluate ab:  \nab=9×5=45  \n13.1  \nx+y-1=1-(1-x)  \nDistribute:  \nx+y-1=1-1+x  \nSubtractx:  \ny-1=1-1  \nSimplify:  \ny-1=0  \nAdd 1:  \ny=1  \n14.200  \n3x²+2x=40  \nMultiply by5:  \n15x²+10x=200  \n15.12 Let e=Ellen's current age and m=Maria'scurrent age.  \nEllen is twice as old as Maria:  \ne=2m  \nIn 6 years,Maria will be 2/3 as  \nold as Ellen:  \nSubstitute e=2m:  \nMultiply by3:  \n3m+18=2(2m+6)  \nDistribute:  \n3m+18=4m+12  \nSubtract 3m and 12:  \n6=m  \nTherefore e=2m=2(6)=12.  \n16.15 First equation:  \n2x-2y=5  \nDivide by2:  \nx-y=2.5  \nSecond equation:  \nx+y=6  \n(x-y)(x+y)=x²-y²=(2.5)(6)=15  \nMultiply:  \nAlternately,we could solve the system using eithersubstitution or linear combination and get x=4.25 andy=1.75,andevaluatex²-y²=(4.25)²-(1.75)²=18.0625-  \n3.0625=15.  \n17.B The revenue is equal to the number of itemssold times the price per item.If the restaurant typicallysells n sandwiches per day,but today sold 50%more,itsold 1.5n sandwiches.If the price p was reduced 30%,today's price is 0.70p.Therefore,the total revenue is  \n(1.5n)(0.70p)=1.05np.  \n\n| 18.B   | 4x(x)-3xy(2x)   |\n| --- | --- |\n| Multiply:   | 4x²-6x²y   |\n| Largest common factor:   | 2x²(2-3y)   |\n\n19.D Although a calculator is permitted for this ques-tion,most calculators willgive an“overflow error”whentrying to calculate numbers like 99100,because they're  \njust too large.However,comparing these numbers isstraightforward if we can express them in a commonformat.  \na=60(99)⁹⁹+30(99)⁹9=90(99)99b=99100=99(99)99c=90(90)⁹9=90(90)⁹9  \n20.A Only statement I is true,by the Commutativeand Associative Laws of Addition.Choosing simple val-ues likex=1,y=2,andz=3will demonstrate that state-ments II and III do not yield true equations.  \n21.C Letx=the number of dollarsDavid had to start.If Carlos started with twice as much money as David,then Carlos started with 2x dollars.After Carlos gaveDavid $12,Carlos had 2x-12 dollars and David hadx+12 dollars.If Carlos stillhad $10 more than David,then  \n2x-12=10+x+12  \nSimplify:  \n2x-12=x+22  \nAdd 12:  \n2x=x+34  \nSubtract x:  \nx=34  \nTherefore,David started with $34 andCarlos started with2($34)=$68,so they had $34+$68=$102 combined tostart.","cbCaivotYBd6ownb","https://ap.wps.com/l/cbCaivotYBd6ownb","pdf",586584,"English","# EXERCISE SET 1 ANSWER KEY\n## Solutions for Problems 1-21","[{\"question\":\"What topics are covered in the answer key?\",\"answer\":\"The key covers simplifying algebraic expressions, solving linear equations and systems, applying distribution, and working through word problems involving age, money, and revenue.\"},{\"question\":\"How are linear equations like 6x-14=40 solved?\",\"answer\":\"The steps shown include adding or subtracting constants to isolate the term with x, then dividing to get the value of x.\"},{\"question\":\"How does the document suggest dealing with comparing extremely large numbers?\",\"answer\":\"It explains that calculators may overflow for expressions like 99100, so rewriting terms into a common format allows straightforward comparison.\"}]","Express Operations1 Answer Key | PDF"]