[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571856-105":53,"doc-detail-571856-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","algebra-cheat-sheets-solving-equations-graphing-writing-equations-quick-reference","algebra-cheat-sheets - Solving Equations, Graphing & Writing Equations Quick Reference","","Quick Reference for solving and manipulating algebraic equations, covering integer addition/subtraction rules, multiplication/division sign rules, and the Golden Rule for equations. Includes steps for solving equations using fractions, distributive property, like terms, collecting variables and constants, and validating via substitution. Provides graphing basics with slope (rise/run), slope-intercept form y=mx+b, and y-intercept/slope identification. Also explains writing equations from slope-intercept form, slope plus a point, and two points, plus standard form and systems of equations methods.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/algebra-cheat-sheets-solving-equations-graphing-writing-equations-quick-reference/571856/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/algebra-cheat-sheets-solving-equations-graphing-writing-equations-quick-reference/571856.png","ImageObject",442,249,{"name":88,"@type":89},"Ezra","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-24","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":47},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are the integer rules for addition and subtraction when solving algebraic equations?","Question",{"text":108,"@type":109},"For addition, if signs match, add numbers and keep the sign; if signs differ, subtract and keep the sign of the number with the largest absolute value. For subtraction, add the opposite (change the subtraction sign to addition and flip the second number’s sign).","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How do you solve an equation involving fractions?",{"text":113,"@type":109},"Multiply every term on both sides by the denominator to clear fractions, then continue with the next steps such as using the distributive property if there are parentheses and combining like terms.",{"name":115,"@type":106,"acceptedAnswer":116},"How do you find the slope and graph using slope-intercept form?",{"text":117,"@type":109},"Choose two points to compute slope as rise/run, assign the sign based on whether the line rises or falls and whether you move up/right or down/left. Identify the y-intercept, plot it, then use the slope’s rise and run to plot a second point and draw the line through both points.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},571856,1792404027,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":47,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":79},1099514068035,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Solving Equations—Quick Reference  \nInteger Rules Addition:  \n• If the signs are the same, add the numbers and keep the sign.  \n• If the signs are different, subtract the numbers and keep the sign of the number with the largest absolute value.  \nSubtraction: Add the opposite  \nKeep—Change—Change  \n• Keep the first number the same.  \n• Change the subtraction sign to addition.  \n• Change the sign of the second number toit’s opposite sign.  \nMultiplication and Division:  \n• If the signs are the same, the answer is positive.  \n• If the signs are different, the answer is negative.  \n\n| \u003Cbr>Golden Rule for Solving Equations:\u003Cbr>Whatever You Do To One Side of the Equation, You Must Do to the Other Side! |  |\n| --- | --- |\n| Combining Like Terms\u003Cbr>Like terms are two or more terms that contain the same variable. |  |\n| Example: 3x, 8x, 9x 2y, 9y, 10y\u003Cbr>3x, 3y\u003Cbr>| are like terms.\u003Cbr>are like terms.\u003Cbr>are NOT like terms because they do NOT have the same variable! |\n\nDistributive Property Examples  \n3(x+5) = 3x +15 Multiply the 3 times x and 5.  \n-2(y –5) = -2y +10 Multiply –2 times y and –5.  \n5(2x –6) = 10x –30 Multiply 5 times 2x and –6.  \nSolving Equations Study Guide  \n1. Does your equation have fractions?  \nYes—Multiply every term (on both sides) by the denominator.  \nNo—Go to Step 2.  \n2. Does your equation involve the distributive property?(Do you see parenthesis?)  \nYes—Rewrite the equation using the distributive property.  \nNo—Go to Step 3.  \n3. On either side, do you have like terms?  \nYes—Rewrite the equation with like terms together. Then combine like terms.  \n(Don’t forget to take the sign in front of each term!)  \nNo– Go to Step 4.  \n4. Do you have variables on both sides of the equation?  \nYes—Add or subtract the terms to get all the variables on one side and all the constantson the other side. Then go to step 6.  \nNo—Go to Step 5.  \n5. At this point, you should have a basic two-step equation. If not go back and recheck your steps above.  \n-Use Addition or Subtraction to remove any constants from the variable side of the equation.  \n(Remember the Golden Rule!)  \n6. Use multiplication or division to remove any coefficients form the variable side of the equation.  \n(Remember the Golden Rule!)  \n7. Check your answer using substitution!  \nCongratulations! You are finished the problem!  \n[Copyright 2009 Algebra-class.com](Copyright 2009 Algebra-class.com)  \nGraphing Equations—Quick Reference  \nSlope= rise run  \n• Calculate the slope by choosing two points on the line.  \n• Count the rise (how far up or down to get to the next point?) This is the numerator.  \n• Count the run (how far left or right to get to the next point?) This is the denominator.  \n•Write the slope as a fraction.  \nSlope = 3/5  \n** Read the graph from left to right. If the line is falling , then the slope is negative.  \nIf the line is rising , the slope is positive.  \n**When counting the rise and run, if you count down or left , then the number is negative. If you count up or right , the number is positive.  \nSlope Intercept Formy = mx +b  \nSlope Y-intercept  \nCopyright © [2009 Algebra-class.com](2009 Algebra-class.com)  \n\n| Graphing Using Slope Intercept Form\u003Cbr>1. Identify the slope and y-intercept in the equation.\u003Cbr>y = 3x-2\u003Cbr>Slope Y-intercept\u003Cbr>|\n| --- |\n| 2. Plot the y-intercept on the graph.\u003Cbr>\u003Cbr>3. From the y-intercept, count the rise and run for the slope. Plot the second point.\u003Cbr>\u003Cbr>4. Draw a line through your two points.\u003Cbr>|\n\nWriting Equations—Quick Reference  \nSlope Intercept Form  \ny = mx +b  \nSlope Y-intercept  \nIf you know the slope (or rate) and the  \ny-intercept (or constant), then you can easily write an equation in slope intercept form.  \nExample: If you have a slope of 3 and  \ny-intercept of-4 , the equation can be written as:  \ny = 3x -4  \nslope y-intercept  \nWriting Equations Given Slope and a  \nPoint  \nIf you are given slope and a point, then you are given m, x , and y for the equation  \ny = mx + b.  \nYou must have slope (m) a","cbCairQ4CMcGUrb3","https://ap.wps.com/l/cbCairQ4CMcGUrb3","pdf",925267,10,"English","# Solving Equations—Quick Reference\n## Integer Rules, Keep-Change-Change, Multiplication/Division Signs\n## Golden Rule and Combining Like Terms\n## Distributive Property Examples\n## Solving Equations Study Guide (Steps 1-7)\n# Graphing Equations—Quick Reference\n## Slope (rise/run) and Sign of Slope\n## Slope Intercept Form and Graphing Procedure\n# Writing Equations—Quick Reference\n## Slope Intercept Form Basics\n## Writing with Slope and a Point\n## Writing with Two Points\n## Standard Form and Constraints\n# Systems of Equations—Quick Reference\n## Methods and Graphing Systems Intro","[{\"question\":\"What are the integer rules for addition and subtraction when solving algebraic equations?\",\"answer\":\"For addition, if signs match, add numbers and keep the sign; if signs differ, subtract and keep the sign of the number with the largest absolute value. For subtraction, add the opposite (change the subtraction sign to addition and flip the second number’s sign).\"},{\"question\":\"How do you solve an equation involving fractions?\",\"answer\":\"Multiply every term on both sides by the denominator to clear fractions, then continue with the next steps such as using the distributive property if there are parentheses and combining like terms.\"},{\"question\":\"How do you find the slope and graph using slope-intercept form?\",\"answer\":\"Choose two points to compute slope as rise/run, assign the sign based on whether the line rises or falls and whether you move up/right or down/left. Identify the y-intercept, plot it, then use the slope’s rise and run to plot a second point and draw the line through both points.\"}]","algebra-cheat-sheets - Solving Equations, Graphing & Writing Equations Quick Reference | PDF",1791924091]