{"id":15733,"date":"2021-10-19T20:51:23","date_gmt":"2021-10-19T20:51:23","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/problem-set-solving-linear-equations-part-i\/"},"modified":"2021-10-22T01:43:38","modified_gmt":"2021-10-22T01:43:38","slug":"problem-set-solving-linear-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/problem-set-solving-linear-equations\/","title":{"raw":"Problem Set: Multi-Step Linear Equations","rendered":"Problem Set: Multi-Step Linear Equations"},"content":{"raw":"<h3>PROBLEM SET<\/h3>\r\nIn the following exercises, solve the linear equation using the general strategy.\r\n\r\n1. [latex]4\\left(y+7\\right)=64[\/latex]\r\n\r\n[reveal-answer q=\"552029\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"552029\"]9[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n2. [latex]9=3\\left(x - 3\\right)[\/latex]\r\n\r\n[reveal-answer q=\"840608\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"840608\"]6[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n3. [latex]14\\left(y - 6\\right)=-42[\/latex]\r\n\r\n[reveal-answer q=\"157692\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"157692\"]3[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n4. [latex]-7\\left(3n+4\\right)=14[\/latex]\r\n\r\n[reveal-answer q=\"67381\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"67381\"]\u22122[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n5. [latex]8\\left(3+3\\text{p}\\right)=0[\/latex]\r\n\r\n[reveal-answer q=\"668664\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"668664\"]\u22121[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n6. [latex]\\Large\\frac{3}{5}\\normalsize\\left(10x - 5\\right)=27[\/latex]\r\n\r\n[reveal-answer q=\"190513\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"190513\"]5[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n7. [latex]4\\left(2.5v - 0.6\\right)=7.6[\/latex]\r\n\r\n[reveal-answer q=\"322191\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"322191\"]0.52[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n8. [latex]0.5\\left(16m+34\\right)=-15[\/latex]\r\n\r\n[reveal-answer q=\"53146\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"53146\"]0.25[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n9. [latex]-\\left(t - 8\\right)=17[\/latex]\r\n\r\n[reveal-answer q=\"828155\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"828155\"]\u22129[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n10. [latex]8\\left(6b - 7\\right)+23=63[\/latex]\r\n\r\n[reveal-answer q=\"895109\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"895109\"]2[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n11. [latex]13+2\\left(m - 4\\right)=17[\/latex]\r\n\r\n[reveal-answer q=\"44817\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"44817\"]6[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n12. [latex]-9+6\\left(5-k\\right)=12[\/latex]\r\n\r\n[reveal-answer q=\"423380\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"423380\"]3\/2[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n13. [latex]18-\\left(9r+7\\right)=-16[\/latex]\r\n\r\n[reveal-answer q=\"316926\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"316926\"]3[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n14. [latex]18 - 2\\left(y - 3\\right)=32[\/latex]\r\n\r\n[reveal-answer q=\"80147\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"80147\"]\u22124[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n15. [latex]3\\left(4n - 1\\right)-2=8n+3[\/latex]\r\n\r\n[reveal-answer q=\"67718\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"67718\"]2[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n16. [latex]5\\left(x - 4\\right)-4x=14[\/latex]\r\n\r\n[reveal-answer q=\"299277\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"299277\"]34[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n17. [latex]5+6\\left(3s - 5\\right)=-3+2\\left(8s - 1\\right)[\/latex]\r\n\r\n[reveal-answer q=\"52907\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"52907\"]10[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n18. [latex]4\\left(x - 1\\right)-8=6\\left(3x - 2\\right)-7[\/latex]\r\n\r\n[reveal-answer q=\"103692\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"103692\"]2[\/hidden-answer]\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>everyday math<\/h3>\r\n<h4><strong>Making a fence<\/strong><\/h4>\r\nJovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is [latex]150[\/latex] feet. The length is [latex]15[\/latex] feet more than the width. Find the width, [latex]w[\/latex], by solving the equation [latex]150=2\\left(w+15\\right)+2w[\/latex].\r\n\r\n[reveal-answer q=\"325402\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"325402\"]30 feet[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<strong>Coins<\/strong> Rhonda has [latex]{$1.90}[\/latex] in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, [latex]n[\/latex], by solving the equation [latex]0.05n+0.10\\left(2n - 1\\right)=1.90[\/latex].\r\n\r\n[reveal-answer q=\"633646\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"633646\"]8 nickels[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\nIn the following exercises, solve the equation by clearing the fractions.\r\n\r\n19. [latex]\\Large\\frac{1}{4}\\normalsize x-\\Large\\frac{1}{2}\\normalsize =-\\Large\\frac{3}{4}[\/latex]\r\n\r\n[reveal-answer q=\"712174\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"712174\"][latex]x = \u22121[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n20. [latex]\\Large\\frac{5}{6}\\normalsize y-\\Large\\frac{2}{3}\\normalsize =-\\Large\\frac{3}{2}[\/latex]\r\n\r\n[reveal-answer q=\"429518\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"429518\"][latex]y = \u22121[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n21. [latex]\\Large\\frac{1}{2}\\normalsize a+\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{3}{4}[\/latex]\r\n\r\n[reveal-answer q=\"298338\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"298338\"][latex]a=\\Large\\frac{3}{4}[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n22. [latex]2=\\Large\\frac{1}{3}\\normalsize x-\\Large\\frac{1}{2}\\normalsize x+\\Large\\frac{2}{3}\\normalsize x[\/latex]\r\n\r\n[reveal-answer q=\"626257\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"626257\"][latex]x = 4[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n23. [latex]\\Large\\frac{1}{4}\\normalsize m-\\Large\\frac{4}{5}\\normalsize m+\\Large\\frac{1}{2}\\normalsize m=-1[\/latex]\r\n\r\n[reveal-answer q=\"918424\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"918424\"][latex]m = 20[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n24. [latex]x+\\Large\\frac{1}{2}\\normalsize =\\Large\\frac{2}{3}\\normalsize x-\\Large\\frac{1}{2}[\/latex]\r\n\r\n[reveal-answer q=\"768211\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"768211\"][latex]x = \u22123[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n25. [latex]\\Large\\frac{1}{3}\\normalsize w+\\Large\\frac{5}{4}\\normalsize =w-\\Large\\frac{1}{4}[\/latex]\r\n\r\n[reveal-answer q=\"711501\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"711501\"][latex]w=\\Large\\frac{9}{4}[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n26. [latex]\\Large\\frac{1}{2}\\normalsize x-\\Large\\frac{1}{4}\\normalsize =\\Large\\frac{1}{12}\\normalsize x+\\Large\\frac{1}{6}[\/latex]\r\n\r\n[reveal-answer q=\"666263\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"666263\"][latex]x = 1[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n27. [latex]\\Large\\frac{1}{3}\\normalsize b+\\Large\\frac{1}{5}\\normalsize =\\Large\\frac{2}{5}\\normalsize b-\\Large\\frac{3}{5}[\/latex]\r\n\r\n[reveal-answer q=\"869289\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"869289\"][latex]b = 12[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n28. [latex]1=\\Large\\frac{1}{6}\\normalsize\\left(12x - 6\\right)[\/latex]\r\n\r\n[reveal-answer q=\"402209\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"402209\"][latex]x = 1[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n29. [latex]\\Large\\frac{1}{2}\\normalsize\\left(x+4\\right)=\\Large\\frac{3}{4}[\/latex]\r\n\r\n[reveal-answer q=\"779746\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"779746\"][latex]x=-\\Large\\frac{5}{2}[\/latex][\/hidden-answer]\r\n<h3><\/h3>\r\nIn the following exercises, solve the equation by clearing the decimals.\r\n\r\n30. [latex]0.9x - 1.25=0.75x+1.75[\/latex]\r\n\r\n[reveal-answer q=\"66192\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"66192\"][latex]x = 20[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n31. [latex]0.10d+0.25\\left(d+5\\right)=4.05[\/latex]\r\n\r\n[reveal-answer q=\"414163\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"414163\"][latex]d = 8[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n32. [latex]0.05\\left(q - 5\\right)+0.25q=3.05[\/latex]\r\n\r\n[reveal-answer q=\"445270\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"445270\"][latex]q = 11[\/latex][\/hidden-answer]\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Everyday math<\/h3>\r\n<strong>Coins<\/strong> Taylor has [latex]{$2.00}[\/latex] in dimes and pennies. The number of pennies is [latex]2[\/latex] more than the number of dimes. Solve the equation [latex]0.10d+0.01\\left(d+2\\right)=2[\/latex] for [latex]d[\/latex], the number of dimes.\r\n\r\n[reveal-answer q=\"950890\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"950890\"][latex]d = 18[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Contribute!<\/h2>\r\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\r\n<a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/1VUly3X5kHn-E5d4QnOLV8iY0mDg1mi_QxUdPaIfoCe0\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>","rendered":"<h3>PROBLEM SET<\/h3>\n<p>In the following exercises, solve the linear equation using the general strategy.<\/p>\n<p>1. [latex]4\\left(y+7\\right)=64[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q552029\">Show Answer<\/span><\/p>\n<div id=\"q552029\" class=\"hidden-answer\" style=\"display: none\">9<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>2. [latex]9=3\\left(x - 3\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q840608\">Show Answer<\/span><\/p>\n<div id=\"q840608\" class=\"hidden-answer\" style=\"display: none\">6<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>3. [latex]14\\left(y - 6\\right)=-42[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q157692\">Show Answer<\/span><\/p>\n<div id=\"q157692\" class=\"hidden-answer\" style=\"display: none\">3<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>4. [latex]-7\\left(3n+4\\right)=14[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q67381\">Show Answer<\/span><\/p>\n<div id=\"q67381\" class=\"hidden-answer\" style=\"display: none\">\u22122<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>5. [latex]8\\left(3+3\\text{p}\\right)=0[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q668664\">Show Answer<\/span><\/p>\n<div id=\"q668664\" class=\"hidden-answer\" style=\"display: none\">\u22121<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>6. [latex]\\Large\\frac{3}{5}\\normalsize\\left(10x - 5\\right)=27[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q190513\">Show Answer<\/span><\/p>\n<div id=\"q190513\" class=\"hidden-answer\" style=\"display: none\">5<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>7. [latex]4\\left(2.5v - 0.6\\right)=7.6[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q322191\">Show Answer<\/span><\/p>\n<div id=\"q322191\" class=\"hidden-answer\" style=\"display: none\">0.52<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>8. [latex]0.5\\left(16m+34\\right)=-15[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q53146\">Show Answer<\/span><\/p>\n<div id=\"q53146\" class=\"hidden-answer\" style=\"display: none\">0.25<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>9. [latex]-\\left(t - 8\\right)=17[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q828155\">Show Answer<\/span><\/p>\n<div id=\"q828155\" class=\"hidden-answer\" style=\"display: none\">\u22129<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>10. [latex]8\\left(6b - 7\\right)+23=63[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q895109\">Show Answer<\/span><\/p>\n<div id=\"q895109\" class=\"hidden-answer\" style=\"display: none\">2<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>11. [latex]13+2\\left(m - 4\\right)=17[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q44817\">Show Answer<\/span><\/p>\n<div id=\"q44817\" class=\"hidden-answer\" style=\"display: none\">6<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>12. [latex]-9+6\\left(5-k\\right)=12[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q423380\">Show Answer<\/span><\/p>\n<div id=\"q423380\" class=\"hidden-answer\" style=\"display: none\">3\/2<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>13. [latex]18-\\left(9r+7\\right)=-16[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q316926\">Show Answer<\/span><\/p>\n<div id=\"q316926\" class=\"hidden-answer\" style=\"display: none\">3<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>14. [latex]18 - 2\\left(y - 3\\right)=32[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q80147\">Show Answer<\/span><\/p>\n<div id=\"q80147\" class=\"hidden-answer\" style=\"display: none\">\u22124<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>15. [latex]3\\left(4n - 1\\right)-2=8n+3[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q67718\">Show Answer<\/span><\/p>\n<div id=\"q67718\" class=\"hidden-answer\" style=\"display: none\">2<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>16. [latex]5\\left(x - 4\\right)-4x=14[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q299277\">Show Answer<\/span><\/p>\n<div id=\"q299277\" class=\"hidden-answer\" style=\"display: none\">34<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>17. [latex]5+6\\left(3s - 5\\right)=-3+2\\left(8s - 1\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q52907\">Show Answer<\/span><\/p>\n<div id=\"q52907\" class=\"hidden-answer\" style=\"display: none\">10<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>18. [latex]4\\left(x - 1\\right)-8=6\\left(3x - 2\\right)-7[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q103692\">Show Answer<\/span><\/p>\n<div id=\"q103692\" class=\"hidden-answer\" style=\"display: none\">2<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>everyday math<\/h3>\n<h4><strong>Making a fence<\/strong><\/h4>\n<p>Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is [latex]150[\/latex] feet. The length is [latex]15[\/latex] feet more than the width. Find the width, [latex]w[\/latex], by solving the equation [latex]150=2\\left(w+15\\right)+2w[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q325402\">Show Answer<\/span><\/p>\n<div id=\"q325402\" class=\"hidden-answer\" style=\"display: none\">30 feet<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong>Coins<\/strong> Rhonda has [latex]{$1.90}[\/latex] in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, [latex]n[\/latex], by solving the equation [latex]0.05n+0.10\\left(2n - 1\\right)=1.90[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q633646\">Show Answer<\/span><\/p>\n<div id=\"q633646\" class=\"hidden-answer\" style=\"display: none\">8 nickels<\/div>\n<\/div>\n<\/div>\n<h3><\/h3>\n<p>In the following exercises, solve the equation by clearing the fractions.<\/p>\n<p>19. [latex]\\Large\\frac{1}{4}\\normalsize x-\\Large\\frac{1}{2}\\normalsize =-\\Large\\frac{3}{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q712174\">Show Answer<\/span><\/p>\n<div id=\"q712174\" class=\"hidden-answer\" style=\"display: none\">[latex]x = \u22121[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>20. [latex]\\Large\\frac{5}{6}\\normalsize y-\\Large\\frac{2}{3}\\normalsize =-\\Large\\frac{3}{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q429518\">Show Answer<\/span><\/p>\n<div id=\"q429518\" class=\"hidden-answer\" style=\"display: none\">[latex]y = \u22121[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>21. [latex]\\Large\\frac{1}{2}\\normalsize a+\\Large\\frac{3}{8}\\normalsize =\\Large\\frac{3}{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q298338\">Show Answer<\/span><\/p>\n<div id=\"q298338\" class=\"hidden-answer\" style=\"display: none\">[latex]a=\\Large\\frac{3}{4}[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>22. [latex]2=\\Large\\frac{1}{3}\\normalsize x-\\Large\\frac{1}{2}\\normalsize x+\\Large\\frac{2}{3}\\normalsize x[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q626257\">Show Answer<\/span><\/p>\n<div id=\"q626257\" class=\"hidden-answer\" style=\"display: none\">[latex]x = 4[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>23. [latex]\\Large\\frac{1}{4}\\normalsize m-\\Large\\frac{4}{5}\\normalsize m+\\Large\\frac{1}{2}\\normalsize m=-1[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q918424\">Show Answer<\/span><\/p>\n<div id=\"q918424\" class=\"hidden-answer\" style=\"display: none\">[latex]m = 20[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>24. [latex]x+\\Large\\frac{1}{2}\\normalsize =\\Large\\frac{2}{3}\\normalsize x-\\Large\\frac{1}{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q768211\">Show Answer<\/span><\/p>\n<div id=\"q768211\" class=\"hidden-answer\" style=\"display: none\">[latex]x = \u22123[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>25. [latex]\\Large\\frac{1}{3}\\normalsize w+\\Large\\frac{5}{4}\\normalsize =w-\\Large\\frac{1}{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q711501\">Show Answer<\/span><\/p>\n<div id=\"q711501\" class=\"hidden-answer\" style=\"display: none\">[latex]w=\\Large\\frac{9}{4}[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>26. [latex]\\Large\\frac{1}{2}\\normalsize x-\\Large\\frac{1}{4}\\normalsize =\\Large\\frac{1}{12}\\normalsize x+\\Large\\frac{1}{6}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q666263\">Show Answer<\/span><\/p>\n<div id=\"q666263\" class=\"hidden-answer\" style=\"display: none\">[latex]x = 1[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>27. [latex]\\Large\\frac{1}{3}\\normalsize b+\\Large\\frac{1}{5}\\normalsize =\\Large\\frac{2}{5}\\normalsize b-\\Large\\frac{3}{5}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q869289\">Show Answer<\/span><\/p>\n<div id=\"q869289\" class=\"hidden-answer\" style=\"display: none\">[latex]b = 12[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>28. [latex]1=\\Large\\frac{1}{6}\\normalsize\\left(12x - 6\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q402209\">Show Answer<\/span><\/p>\n<div id=\"q402209\" class=\"hidden-answer\" style=\"display: none\">[latex]x = 1[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>29. [latex]\\Large\\frac{1}{2}\\normalsize\\left(x+4\\right)=\\Large\\frac{3}{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q779746\">Show Answer<\/span><\/p>\n<div id=\"q779746\" class=\"hidden-answer\" style=\"display: none\">[latex]x=-\\Large\\frac{5}{2}[\/latex]<\/div>\n<\/div>\n<h3><\/h3>\n<p>In the following exercises, solve the equation by clearing the decimals.<\/p>\n<p>30. [latex]0.9x - 1.25=0.75x+1.75[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q66192\">Show Answer<\/span><\/p>\n<div id=\"q66192\" class=\"hidden-answer\" style=\"display: none\">[latex]x = 20[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>31. [latex]0.10d+0.25\\left(d+5\\right)=4.05[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q414163\">Show Answer<\/span><\/p>\n<div id=\"q414163\" class=\"hidden-answer\" style=\"display: none\">[latex]d = 8[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>32. [latex]0.05\\left(q - 5\\right)+0.25q=3.05[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q445270\">Show Answer<\/span><\/p>\n<div id=\"q445270\" class=\"hidden-answer\" style=\"display: none\">[latex]q = 11[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Everyday math<\/h3>\n<p><strong>Coins<\/strong> Taylor has [latex]{$2.00}[\/latex] in dimes and pennies. The number of pennies is [latex]2[\/latex] more than the number of dimes. Solve the equation [latex]0.10d+0.01\\left(d+2\\right)=2[\/latex] for [latex]d[\/latex], the number of dimes.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q950890\">Show Answer<\/span><\/p>\n<div id=\"q950890\" class=\"hidden-answer\" style=\"display: none\">[latex]d = 18[\/latex]<\/div>\n<\/div>\n<\/div>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/1VUly3X5kHn-E5d4QnOLV8iY0mDg1mi_QxUdPaIfoCe0\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-15733\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"f77ff678-8391-42e5-aee5-8027d90fd754","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-15733","chapter","type-chapter","status-publish","hentry"],"part":10990,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15733","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/167848"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15733\/revisions"}],"predecessor-version":[{"id":15861,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15733\/revisions\/15861"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/10990"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15733\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=15733"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=15733"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=15733"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=15733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}