[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-508231-105":59,"doc-detail-508231-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","compound-inequalities-practice-worksheet","Compound Inequalities - Practice Worksheet","","Compound Inequalities practice worksheet focused on solving “and” and “or” compound inequalities. It explains that an “and” compound inequality represents two conditions true at the same time and is solved as a double inequality by applying the same operation to all parts, while noting to flip inequality signs when multiplying or dividing by a negative. Includes practice problems, word problems, an answer key, and step-by-step solution guidance.",{"@graph":69,"@context":122},[70,84,105],{"@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/compound-inequalities-practice-worksheet/508231/",{"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/compound-inequalities-practice-worksheet/508231.png","ImageObject",300,407,{"name":92,"@type":93},"Anna Hans","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-05",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you solve an “and” compound inequality like 3 \u003C x \u003C 7?","Question",{"text":112,"@type":113},"Treat it as a double inequality and solve both parts at once by applying the same operation to all terms. Keep both inequalities true simultaneously.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What should you do when you multiply or divide both sides by a negative number?",{"text":117,"@type":113},"Flip the inequality signs after multiplying or dividing by a negative. This keeps the inequality direction correct.",{"name":119,"@type":110,"acceptedAnswer":120},"How are word problems with inequalities handled on this worksheet?",{"text":121,"@type":113},"Translate the situation into an inequality (or compound inequality), then solve for the variable and interpret the solution in context (such as temperature or storage sensor ranges).","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},508231,1791369680,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":39,"preview_page_count":4},5909892332657,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Practice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nCompound Inequalities  \n\n| Name:   | D | ate:   | S | core:   / 18 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nAn “and” compound inequality such as 3 \u003C x 􀀔 7 means both parts are true at once – solve it as a double inequality, doing the same operation to all three parts. An “or” inequality means at least one part is true. Remember to 􀀃ip the signs if you multiply or divide by a negative.  \n▷ Example: Solve 1 􀀔 2x + 3 \u003C 9. Work: Subtract 3 from all three parts: 􀀀2 􀀔 2x \u003C 6. Divide every part by 2: 􀀀1 􀀔 x \u003C 3.⋆ Answer: 􀀀1 􀀔 x \u003C 3  \n􀀀3 􀀀2 􀀀1 0 1 2 3  \n􀀀1 􀀔 x \u003C 3: closed at 􀀀1, open at 3.  \n♦ Practice Problems  \nSolve each compound inequality.  \n1. 2 \u003C x + 1 \u003C 5 8. 3 􀀔 2x 􀀀 1 􀀔 9  \n2. 􀀀3 􀀔 x 􀀀 2 􀀔 1  \n9. 􀀀4 􀀔 2x 􀀔 6  \n3. 4 \u003C 2x \u003C 10 10. 5 \u003C x + 3 \u003C 9  \n4. 6 􀀔 3x 􀀔 18 11. 4 􀀔 4x 􀀔 12  \n5. 1 􀀔 x + 4 􀀔 7 12. 􀀀1 \u003C 3x + 2 \u003C 11  \n6. 0 \u003C 2x + 2 \u003C 8  \n13. 0 􀀔 5x 􀀔 20  \n7. 􀀀5 \u003C x 􀀀 1 \u003C 2  \n14. 􀀀6 \u003C 2x 􀀀 2 \u003C 4  \n♦ Word Problems  \n15. A number plus 3 is between 5 and 10. Write and solve a compound inequality.  \n16. Twice a number is at least 4 and at most 16. Find the numbers.  \n17. A temperature x satis􀀂es 10 􀀔 x 􀀀 5 􀀔 25. Solve for x.  \n18. A storage room sensor reads x + 1 degrees. The safe range is above 􀀀2 degrees and at most 4 degrees. Write the solution for x.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n| 1. | 1 \u003C x \u003C 4\u003Cbr>| 7.  􀀀4 \u003C x \u003C 3  | 13. | 0 􀀔 x 􀀔 4\u003Cbr>|\n| --- | --- | --- | --- | --- |\n| 2. | 􀀀1 􀀔 x 􀀔 3\u003Cbr>| 8. 2 􀀔 x 􀀔 5\u003Cbr>| 14. |  􀀀2 \u003C x \u003C 3  |\n| 3. | 2 \u003C x \u003C 5\u003Cbr>| 9. 􀀀2 􀀔 x 􀀔 3\u003Cbr>| 15. | 2 \u003C x \u003C 7\u003Cbr>|\n| 4. |  2 􀀔 x 􀀔 6  | 10. 2 \u003C x \u003C 6\u003Cbr>| 16. |  2 􀀔 x 􀀔 8  |\n| 5. |  􀀀3 􀀔 x 􀀔 3  | 11. 1 􀀔 x 􀀔 3\u003Cbr>| 17. |  15 􀀔 x 􀀔 30  |\n| 6. | 􀀀1 \u003C x \u003C 3\u003Cbr>| 12. 􀀀1 \u003C x \u003C 3\u003Cbr>| 18. |  􀀀3 \u003C x 􀀔 3  |\n\nStep-by-Step Explanations  \n1. Start by naming the process: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Subtract 1 from all parts: 1 \u003C x \u003C 4. So the 􀀂nal answer is 1 \u003C x \u003C 4.  \n2. A good way to think about this is: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Add 2 to all parts: 􀀀1 􀀔 x 􀀔 3. So the 􀀂nal answer is 􀀀1 􀀔 x 􀀔 3.  \n3. Step by step: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Divide all parts by 2: 2 \u003C x \u003C 5. So the 􀀂nal answer is 2 \u003C x \u003C 5.  \n4. Take it one move at a time: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Divide all parts by 3: 2 􀀔 x 􀀔 ","cbCaimnKNcMVeD2X","https://ap.wps.com/l/cbCaimnKNcMVeD2X","pdf",111403,"English","# Quick Review and Helpful Hints\n# Practice Problems\n# Word Problems\n# Answer Keys\n# Step-by-Step Explanations","[{\"question\":\"How do you solve an “and” compound inequality like 3 \\u003c x \\u003c 7?\",\"answer\":\"Treat it as a double inequality and solve both parts at once by applying the same operation to all terms. Keep both inequalities true simultaneously.\"},{\"question\":\"What should you do when you multiply or divide both sides by a negative number?\",\"answer\":\"Flip the inequality signs after multiplying or dividing by a negative. This keeps the inequality direction correct.\"},{\"question\":\"How are word problems with inequalities handled on this worksheet?\",\"answer\":\"Translate the situation into an inequality (or compound inequality), then solve for the variable and interpret the solution in context (such as temperature or storage sensor ranges).\"}]","Compound Inequalities - Practice Worksheet | PDF",1791213415]