[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-274527-105":59,"doc-detail-274527-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","chang-learning-shsat-lesson-11-inequality-word-problems","Chang Learning SHSAT Lesson 11 - Inequality Word Problems","","Focuses on solving SHSAT-level algebra inequalities and translating inequality language into mathematical statements. Covers the core rule for reversing inequality direction when multiplying or dividing by a negative number, then applies inverse operations to find solution sets. Includes worked examples and classwork problems that practice inequality solving and choosing correct inequality forms for word situations involving savings, pages read, taxi cost, profits, and spending limits.",{"@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/chang-learning-shsat-lesson-11-inequality-word-problems/274527/",{"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/chang-learning-shsat-lesson-11-inequality-word-problems/274527.png","ImageObject",300,407,{"name":92,"@type":93},"Maya Linwood","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-15",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 rule must be remembered when multiplying or dividing an inequality by a negative number?","Question",{"text":113,"@type":114},"Flip the direction of the inequality symbol on both sides when the operation involves a negative number.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you solve an inequality like 2(x) - 8 \u003C 11 for x?",{"text":118,"@type":114},"Use inverse operations as in equations: add 8 to both sides, then divide by 2. The result gives the solution set.",{"name":120,"@type":111,"acceptedAnswer":121},"How can you represent a word problem as an inequality?",{"text":122,"@type":114},"Translate the scenario into an expression and use inequality wording such as “at least,” “at most,” “no more than,” or “fewer than” to choose the correct inequality sign before solving.","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},274527,1789478408,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":41},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Name: Date:  \nChang Learning SHSAT Lesson 11: Inequality Word Problems  \nInequality Word Problems  \nProblems with inequalities follow the same algebraic rules as those with equalities. When multiplying or dividing by a negative value, remember to “FLIP” the direction of the inequality symbol as you complete the operation on both sides.  \nExamples: The following examples are inequalities that follow the rules of algebra. Below are examples of problems of SHSAT level algebraic inequalities.  \n\n| Problem \\#1: An inequality is 2(x) -8 \u003C 11. Solve for x. |\n| --- |\n| Solution: Use the same inverse operation rules as with an equation.\u003Cbr>\u003Cbr>2􀕠 − 8 \u003C 11 \u003Cbr>Algebra Step 2(x) \u003C 19\u003Cbr>x \u003C 9.5 Add 8 to both sides Divide by 2\u003Cbr>Answer : The solution set is x \u003C 9.5 |\n\n\n| Problem \\#2: On Saturday, Maya read at least 5 fewer than 3 times as many pages in her book as she did on Friday. On Saturday she read 58 pages. How many pages did Maya read on Friday? |\n| --- |\n| Solution:\u003Cbr>(􀕁􀕉􀕜􀕝􀕚􀕌􀕉􀕡) ≥ 3 (􀔴􀕚􀕑􀕌􀕉􀕡) − 5\u003Cbr>58 = 3 (􀔴) − 5\u003Cbr>63 = 3 (􀔴)\u003Cbr>21 = 􀔴\u003Cbr>ANSWER: 􀔽􀕖 􀔴􀕚􀕑􀕌􀕉􀕡, 􀔻􀕉􀕡􀕉 ℎ􀕉􀕌 􀕚􀕍􀕉􀕌 21 􀕘􀕉􀕏􀕍􀕛 􀕗􀕚 􀕔􀕍􀕛􀕛 . |\n\nSHSAT Mathematics Lesson \\#11 Page 1  \nName: Date:  \nChang Learning SHSAT Lesson 11: Inequality Word Problems  \n\n| Problem \\#3: A taxi driver charges a flat fee of $2.00 for the first ⅕ mile and plus $0.75 per additional ⅕ mile. The tip is included in the mileage rate. Sven has only $35.00 to pay for a taxi ride. How many miles at most can Sven ride in the taxi? |\n| --- |\n| Solution:\u003Cbr>2 + $0 . 75 (5􀕕 − 1) ≤ $35 . 00\u003Cbr>2 + 3. 75􀕕 − 0. 75) ≤ $35 . 00\u003Cbr>1. 25 + $3 . 75􀕕 ≤ $35 . 00 $3 . 75􀕕 ≤ $33 . 75\u003Cbr>Answer : The solution set is m ≤ 9. Sven can go up to 9 miles in the taxi. |\n\nSHSAT Mathematics Lesson \\#11 Page 2  \nName: Date:  \nChang Learning SHSAT Lesson 11: Inequality Word Problems  \nSHSAT Lesson \\#11 Classwork: Inequality Word Problems  \n\n| 1. What is a solution to the inequality 3􀕠 + 9 ≥ 21? | A. 5\u003Cbr>B. 3\u003Cbr>C. 0\u003Cbr>D. − 2\u003Cbr>E. − 3 |\n| --- | --- |\n| 2. All three statements are true for “a” and “b”\u003Cbr>~~ ~~􀕉􀕊~~ ~~ \u003C ~~ ~~􀕊􀕉~~ ~~ 􀕉2 = 2􀕉 􀕉􀕊 = 18\u003Cbr>what is the value of b ? | A. 2\u003Cbr>B. 3\u003Cbr>C. 6\u003Cbr>D. 9\u003Cbr>E. 18 |\n| 3. Aaron found the solution to a problem. Which values are all part of the solution set for the inequality x \u003C 35 ? | A. {34,35,36}\u003Cbr>B. {0,30,60}\u003Cbr>C. {-5,-4,35)\u003Cbr>D. {21,32,33}\u003Cbr>E. {40,30,15} |\n| 4. If (2􀕠 + 1) \u003C 9, then for all possible values of x that make this inequality true, | A. 􀕠 \u003C 8\u003Cbr>B. 􀕠 > 8\u003Cbr>C. 􀕠 > 4\u003Cbr>D. 􀕠 \u003C 4\u003Cbr>E. 􀕠 > ~~ ~~14~~ ~~ |\n| 5. If (15 − 2􀕠) \u003C 7, then for all possible values of x, what values make this inequality true ? | A. 􀕠 \u003C 8\u003Cbr>B. 􀕠 > 8\u003Cbr>C. 􀕠 > 4\u003Cbr>D. 􀕠 \u003C 4\u003Cbr>E. 􀕠 > ~~ ~~14~~ ~~ |\n| 6. Which of the following is equivalent to the inequality 12 \u003C 􀕠 + 4 ? | A. 􀕠 \u003C 8\u003Cbr>B. 􀕠 > 8\u003Cbr>C. 􀕠 > − 8\u003Cbr>D. 􀕠 > 16\u003Cbr>E. 􀕠 \u003C 16 |\n\nSHSAT Mathematics Lesson \\#11 Page 3  \nName: Date:  \nChang Learning SHSAT Lesson 11: Inequality Word Problems  \nSHSAT Lesson \\#11: Classwork (continued)  \n\n| 7. Sammy earns $20 per day plus $6 for every sale he makes. On Friday, he wants to earn at least $50. Which describes the number of sales he needs to make to reach his goal? | A. At least 5 sales\u003Cbr>B. At most 5 sales\u003Cbr>C. At least 6 sales\u003Cbr>D. At most 6 sales\u003Cbr>E. No more than 8 sales |\n| --- | --- |\n| 8. Line ABCD has 􀔾􀕗􀕑􀕖􀕜 􀔯 = − 5, 􀔾􀕗􀕑􀕖􀕜 􀔰 = − 2, and also 􀔾􀕗􀕑􀕖􀕜 􀔱 = 1 􀕉􀕖􀕌 􀔾􀕗􀕑􀕖􀕜 􀔲 = 6.\u003Cbr>How much longer is BD than AC ? (Draw it!) | A. 0\u003Cbr>B. 1\u003Cbr>C. 2\u003Cbr>D. 3\u003Cbr>E. 4 |\n| 9. If x is greater than ~~ 1~~2~~ ~~ but less than 1, which of the following has the largest value ? | A. 3􀕠 + 1 2\u003Cbr>B. 􀕠 C. 1􀕠~~ ~~\u003Cbr>D. 1 − 􀕠\u003Cbr>E. 􀕠 3 |\n| 10. What integer(s) satisfies the following equations\u003Cbr>􀕠2 ≥ 0 􀕉􀕖􀕌 􀕠 ≤ 0 ? | A. 1\u003Cbr>B. 0\u003Cbr>C. No solutions\u003Cbr>D. Any negative integer E. Cannot be determined |\n| 11. Sarvananda saved ~~ ~~35~~ ~~ of the money he earned doing yard work. He saved $120 in all. How much money did he earn doing yard work ? | A. $150\u003Cbr>B. $200\u003Cbr>C. $225\u003Cbr>D. $300\u003Cbr>E. $450 |\n| 12. The cafeteri","cbCaiqZVmVEbj8yO","https://ap.wps.com/l/cbCaiqZVmVEbj8yO","pdf",177929,12,"English","# Inequality Word Problems\n## Key inequality rule (flip on negative)\n## Worked examples\n## Classwork practice problems","[{\"question\":\"What rule must be remembered when multiplying or dividing an inequality by a negative number?\",\"answer\":\"Flip the direction of the inequality symbol on both sides when the operation involves a negative number.\"},{\"question\":\"How do you solve an inequality like 2(x) - 8 \\u003c 11 for x?\",\"answer\":\"Use inverse operations as in equations: add 8 to both sides, then divide by 2. The result gives the solution set.\"},{\"question\":\"How can you represent a word problem as an inequality?\",\"answer\":\"Translate the scenario into an expression and use inequality wording such as “at least,” “at most,” “no more than,” or “fewer than” to choose the correct inequality sign before solving.\"}]","Chang Learning SHSAT Lesson 11 - Inequality Word Problems | PDF"]