{"id":1592,"date":"2021-12-02T19:38:40","date_gmt":"2021-12-03T00:38:40","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-4\/"},"modified":"2022-11-02T10:36:48","modified_gmt":"2022-11-02T14:36:48","slug":"answer-key-2-4","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-4\/","title":{"raw":"Answer Key 2.4","rendered":"Answer Key 2.4"},"content":{"raw":"
    \n \t
  1. [latex]\\left(\\dfrac{3}{5}\\left(1 + p\\right) = \\dfrac{21}{20}\\right)(20)[\/latex]\n[latex]\\dfrac{3}{\\cancel{5}1}\\cdot \\cancel{20 }4(1 + p) = \\dfrac{21}{\\cancel{20}1}\\cdot \\cancel{20} [\/latex]\n[latex]\\begin{array}{rrrrr}\n12&+&12p&=&\\phantom{-}21 \\\\\n-12&&&&-12 \\\\\n\\hline\n&&\\dfrac{12p}{12}&=&\\dfrac{9}{12} \\\\ \\\\\n&&p&=&\\dfrac{3}{4}\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\left(-\\dfrac{1}{2} = \\dfrac{3k}{2} + \\dfrac{3}{2}\\right)(2)[\/latex]\n[latex]\\begin{array}{rrrrr}\n-1&=&3k&+&3 \\\\\n-3&&&-&3 \\\\\n\\hline\n\\dfrac{-4}{3}&=&\\dfrac{3k}{3}&& \\\\ \\\\\nk&=&-\\dfrac{4}{3}&&\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\left(0 = -\\dfrac{5}{4}x+\\dfrac{6}{4}\\right)(4)[\/latex]\n[latex] \\begin{array}{rrlrr}\n0&=&-5x&+&6 \\\\\n+5x&&+5x&& \\\\\n\\hline\n\\dfrac{5x}{5}&=&\\dfrac{6}{5}&& \\\\ \\\\\nx&=&\\dfrac{6}{5}&&\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\left(\\dfrac{3n}{2} - 8 = -\\dfrac{29}{12}\\right)(12)[\/latex]\n[latex] \\begin{array}{rrrrr}\n18n&-&96&=&-29 \\\\\n&+&96&&+96 \\\\\n\\hline\n&&\\dfrac{18n}{18}&=&\\dfrac{67}{18} \\\\ \\\\\n&&n&=&\\dfrac{67}{18}\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]\\left(\\dfrac{3}{4} - \\dfrac{5}{4}m = \\dfrac{108}{24}\\right)(24)[\/latex]\n[latex] \\begin{array}{rrrrr}\n18&-&30m&=&108 \\\\\n-18&&&&-18 \\\\\n\\hline\n&&\\dfrac{-30m}{-30}&=&\\dfrac{90}{-30} \\\\ \\\\\n&&m&=&-3\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]\\left(\\dfrac{11}{4} + \\dfrac{3}{4}r = \\dfrac{160}{32}\\right)(32)[\/latex]\n[latex]\\begin{array}{crcrr}\n11\\cdot 8&+&3r\\cdot 8&=&160 \\\\\n\\phantom{-}88&+&24r&=&160 \\\\\n-88&&&&-88 \\\\\n\\hline\n&&\\dfrac{24r}{24}&=&\\dfrac{72}{24} \\\\ \\\\\n&&r&=&3\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\left(2b + \\dfrac{9}{5} = -\\dfrac{11}{5}\\right)(5) [\/latex]\n[latex]\\begin{array}{rrrrr}\n10b&+&9&=&-11 \\\\\n&-&9&&-9 \\\\\n\\hline\n&&\\dfrac{10b}{10}&=&\\dfrac{-20}{10} \\\\ \\\\\n&&b&=&-2\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\left(\\dfrac{3}{2} - \\dfrac{7v}{4} = -\\dfrac{9}{8}\\right)(8)[\/latex]\n[latex]\\begin{array}{rrrrr}\n3\\cdot 4&-&7r\\cdot 2&=&-9 \\\\\n\\phantom{-}12&-&14r&=&-9 \\\\\n-12&&&&-12 \\\\\n\\hline\n&&\\dfrac{-14r}{-14}&=&\\dfrac{-21}{-14} \\\\ \\\\\n&&r&=&\\dfrac{3}{2}\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\left(\\dfrac{21n}{6}+\\dfrac{3}{2} = \\dfrac{3}{2}\\right)(6)[\/latex]\n[latex] \\begin{array}{rrrrr}\n\\dfrac{21n}{6}&+&3\\cdot 3&=&3\\cdot 3 \\\\\n&-&9&&-9 \\\\\n\\hline\n&&\\dfrac{21n}{6}&=&0 \\\\ \\\\\n&&n&=&0\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\left(\\dfrac{41}{9} = \\dfrac{5}{2}x+\\dfrac{10}{6} - \\dfrac{1}{3}x\\right)(18)[\/latex]\n[latex]\\begin{array}{rrlrrrr}\n41\\cdot 2&=&5x\\cdot 9&+&10\\cdot 3&-&x\\cdot 6 \\\\\n82&=&45x&+&30&-&6x \\\\\n-30&&&-&30&& \\\\\n\\hline\n\\dfrac{52}{39}&=&\\dfrac{39x}{39}&&&& \\\\ \\\\\nx&=&\\dfrac{4}{3}&&&&\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\left(-a + \\dfrac{40a}{12}-\\dfrac{5}{4}= -\\dfrac{19}{4}\\right)(12)[\/latex]\n[latex] \\begin{array}{rrrrrrr}\n-12a&+&40a&-&15&=&-57 \\\\\n&&&+&15&&+15 \\\\\n\\hline\n&&&&\\dfrac{28a}{28}&=&\\dfrac{-42}{28} \\\\ \\\\\n&&&&a&=&-\\dfrac{3}{2}\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\left(-\\dfrac{7k}{12}+\\dfrac{1}{3}-\\dfrac{10k}{3}=-\\dfrac{13}{8} \\right)(24)[\/latex]\n[latex]\\begin{array}{rrrrrrr}\n-14k&+&8&-&80k&=&-39 \\\\\n&-&8&&&&-8 \\\\\n\\hline\n&&&&\\dfrac{-94k}{-94}&=&\\dfrac{-47}{-94} \\\\ \\\\\n&&&&k&=&\\dfrac{1}{2}\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\left(\\dfrac{55}{6} = -\\dfrac{15p}{4}+\\dfrac{25}{6}\\right)(12)[\/latex]\n[latex] \\begin{array}{rrlrr}\n110&=&-45p&+&50 \\\\\n-50&&&-&50 \\\\\n\\hline\n\\dfrac{60}{-45}&=&\\dfrac{-45p}{-45}&& \\\\ \\\\\np&=&-\\dfrac{4}{3}&&\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\left(-\\dfrac{2x}{6}+\\dfrac{3}{8}-\\dfrac{7x}{2}=-\\dfrac{83}{24}\\right)(24)[\/latex]\n[latex]\\begin{array}{rrrrrrr}\n-8x&+&9&-&84x&=&-83 \\\\\n&-&9&&&&-9 \\\\\n\\hline\n&&&&\\dfrac{-92x}{-92}&=&\\dfrac{-92}{-92} \\\\ \\\\\n&&&&x&=&1\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\left(-\\dfrac{5}{8}=\\dfrac{5}{4}r-\\dfrac{15}{8}\\right)(8)[\/latex]\n[latex] \\begin{array}{rrlrr}\n-5&=&10r&-&15 \\\\\n+15&&&+&15 \\\\\n\\hline\n\\dfrac{10}{10}&=&\\dfrac{10r}{10}&& \\\\ \\\\\nr&=&1&&\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\left(\\dfrac{1}{12}=\\dfrac{4x}{3}+\\dfrac{5x}{3}-\\dfrac{35}{12}\\right)(12) [\/latex]\n[latex] \\begin{array}{rrlrrrr}\n1&=&16x&+&20x&-&35 \\\\\n+35&&&&&+&35 \\\\\n\\hline\n\\dfrac{36}{36}&=&\\dfrac{36x}{36}&&&& \\\\ \\\\\nx&=&1&&&&\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\left(-\\dfrac{11}{3}+\\dfrac{3b}{2}=\\dfrac{5b}{2}-\\dfrac{25}{6}\\right)(6) [\/latex]\n[latex]\\begin{array}{rrrrrrr}\n-22&+&9b&=&15b&-&25 \\\\\n+22&-&15b&&-15b&+&22 \\\\\n\\hline\n&&\\dfrac{-6b}{-6}&=&\\dfrac{-3}{-6}&& \\\\ \\\\\n&&b&=&\\dfrac{1}{2}&&\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]\\left(\\dfrac{7}{6}-\\dfrac{4n}{3}=-\\dfrac{3n}{2}+2n+3\\right)(6)[\/latex]\n[latex]\\begin{array}{rrrrlrrrr}\n7&-&8n&=&-9n&+&12n&+&18 \\\\\n-7&+&9n&&+9n&-&12n&-&7 \\\\\n&-&12n&&&&&& \\\\\n\\hline\n&&\\dfrac{-11n}{-11}&=&\\dfrac{11}{-11}&&&& \\\\ \\\\\n&&n&=&-1&&&&\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\left(\\dfrac{3}{5}\\left(1 + p\\right) = \\dfrac{21}{20}\\right)(20)[\/latex]
      \n[latex]\\dfrac{3}{\\cancel{5}1}\\cdot \\cancel{20 }4(1 + p) = \\dfrac{21}{\\cancel{20}1}\\cdot \\cancel{20}[\/latex]
      \n[latex]\\begin{array}{rrrrr} 12&+&12p&=&\\phantom{-}21 \\\\ -12&&&&-12 \\\\ \\hline &&\\dfrac{12p}{12}&=&\\dfrac{9}{12} \\\\ \\\\ &&p&=&\\dfrac{3}{4} \\end{array}[\/latex]<\/li>\n
    2. [latex]\\left(-\\dfrac{1}{2} = \\dfrac{3k}{2} + \\dfrac{3}{2}\\right)(2)[\/latex]
      \n[latex]\\begin{array}{rrrrr} -1&=&3k&+&3 \\\\ -3&&&-&3 \\\\ \\hline \\dfrac{-4}{3}&=&\\dfrac{3k}{3}&& \\\\ \\\\ k&=&-\\dfrac{4}{3}&& \\end{array}[\/latex]<\/li>\n
    3. [latex]\\left(0 = -\\dfrac{5}{4}x+\\dfrac{6}{4}\\right)(4)[\/latex]
      \n[latex]\\begin{array}{rrlrr} 0&=&-5x&+&6 \\\\ +5x&&+5x&& \\\\ \\hline \\dfrac{5x}{5}&=&\\dfrac{6}{5}&& \\\\ \\\\ x&=&\\dfrac{6}{5}&& \\end{array}[\/latex]<\/li>\n
    4. [latex]\\left(\\dfrac{3n}{2} - 8 = -\\dfrac{29}{12}\\right)(12)[\/latex]
      \n[latex]\\begin{array}{rrrrr} 18n&-&96&=&-29 \\\\ &+&96&&+96 \\\\ \\hline &&\\dfrac{18n}{18}&=&\\dfrac{67}{18} \\\\ \\\\ &&n&=&\\dfrac{67}{18} \\end{array}[\/latex]<\/li>\n
    5. [latex]\\left(\\dfrac{3}{4} - \\dfrac{5}{4}m = \\dfrac{108}{24}\\right)(24)[\/latex]
      \n[latex]\\begin{array}{rrrrr} 18&-&30m&=&108 \\\\ -18&&&&-18 \\\\ \\hline &&\\dfrac{-30m}{-30}&=&\\dfrac{90}{-30} \\\\ \\\\ &&m&=&-3 \\end{array}[\/latex]<\/li>\n
    6. [latex]\\left(\\dfrac{11}{4} + \\dfrac{3}{4}r = \\dfrac{160}{32}\\right)(32)[\/latex]
      \n[latex]\\begin{array}{crcrr} 11\\cdot 8&+&3r\\cdot 8&=&160 \\\\ \\phantom{-}88&+&24r&=&160 \\\\ -88&&&&-88 \\\\ \\hline &&\\dfrac{24r}{24}&=&\\dfrac{72}{24} \\\\ \\\\ &&r&=&3 \\end{array}[\/latex]<\/li>\n
    7. [latex]\\left(2b + \\dfrac{9}{5} = -\\dfrac{11}{5}\\right)(5)[\/latex]
      \n[latex]\\begin{array}{rrrrr} 10b&+&9&=&-11 \\\\ &-&9&&-9 \\\\ \\hline &&\\dfrac{10b}{10}&=&\\dfrac{-20}{10} \\\\ \\\\ &&b&=&-2 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\left(\\dfrac{3}{2} - \\dfrac{7v}{4} = -\\dfrac{9}{8}\\right)(8)[\/latex]
      \n[latex]\\begin{array}{rrrrr} 3\\cdot 4&-&7r\\cdot 2&=&-9 \\\\ \\phantom{-}12&-&14r&=&-9 \\\\ -12&&&&-12 \\\\ \\hline &&\\dfrac{-14r}{-14}&=&\\dfrac{-21}{-14} \\\\ \\\\ &&r&=&\\dfrac{3}{2} \\end{array}[\/latex]<\/li>\n
    9. [latex]\\left(\\dfrac{21n}{6}+\\dfrac{3}{2} = \\dfrac{3}{2}\\right)(6)[\/latex]
      \n[latex]\\begin{array}{rrrrr} \\dfrac{21n}{6}&+&3\\cdot 3&=&3\\cdot 3 \\\\ &-&9&&-9 \\\\ \\hline &&\\dfrac{21n}{6}&=&0 \\\\ \\\\ &&n&=&0 \\end{array}[\/latex]<\/li>\n
    10. [latex]\\left(\\dfrac{41}{9} = \\dfrac{5}{2}x+\\dfrac{10}{6} - \\dfrac{1}{3}x\\right)(18)[\/latex]
      \n[latex]\\begin{array}{rrlrrrr} 41\\cdot 2&=&5x\\cdot 9&+&10\\cdot 3&-&x\\cdot 6 \\\\ 82&=&45x&+&30&-&6x \\\\ -30&&&-&30&& \\\\ \\hline \\dfrac{52}{39}&=&\\dfrac{39x}{39}&&&& \\\\ \\\\ x&=&\\dfrac{4}{3}&&&& \\end{array}[\/latex]<\/li>\n
    11. [latex]\\left(-a + \\dfrac{40a}{12}-\\dfrac{5}{4}= -\\dfrac{19}{4}\\right)(12)[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} -12a&+&40a&-&15&=&-57 \\\\ &&&+&15&&+15 \\\\ \\hline &&&&\\dfrac{28a}{28}&=&\\dfrac{-42}{28} \\\\ \\\\ &&&&a&=&-\\dfrac{3}{2} \\end{array}[\/latex]<\/li>\n
    12. [latex]\\left(-\\dfrac{7k}{12}+\\dfrac{1}{3}-\\dfrac{10k}{3}=-\\dfrac{13}{8} \\right)(24)[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} -14k&+&8&-&80k&=&-39 \\\\ &-&8&&&&-8 \\\\ \\hline &&&&\\dfrac{-94k}{-94}&=&\\dfrac{-47}{-94} \\\\ \\\\ &&&&k&=&\\dfrac{1}{2} \\end{array}[\/latex]<\/li>\n
    13. [latex]\\left(\\dfrac{55}{6} = -\\dfrac{15p}{4}+\\dfrac{25}{6}\\right)(12)[\/latex]
      \n[latex]\\begin{array}{rrlrr} 110&=&-45p&+&50 \\\\ -50&&&-&50 \\\\ \\hline \\dfrac{60}{-45}&=&\\dfrac{-45p}{-45}&& \\\\ \\\\ p&=&-\\dfrac{4}{3}&& \\end{array}[\/latex]<\/li>\n
    14. [latex]\\left(-\\dfrac{2x}{6}+\\dfrac{3}{8}-\\dfrac{7x}{2}=-\\dfrac{83}{24}\\right)(24)[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} -8x&+&9&-&84x&=&-83 \\\\ &-&9&&&&-9 \\\\ \\hline &&&&\\dfrac{-92x}{-92}&=&\\dfrac{-92}{-92} \\\\ \\\\ &&&&x&=&1 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\left(-\\dfrac{5}{8}=\\dfrac{5}{4}r-\\dfrac{15}{8}\\right)(8)[\/latex]
      \n[latex]\\begin{array}{rrlrr} -5&=&10r&-&15 \\\\ +15&&&+&15 \\\\ \\hline \\dfrac{10}{10}&=&\\dfrac{10r}{10}&& \\\\ \\\\ r&=&1&& \\end{array}[\/latex]<\/li>\n
    16. [latex]\\left(\\dfrac{1}{12}=\\dfrac{4x}{3}+\\dfrac{5x}{3}-\\dfrac{35}{12}\\right)(12)[\/latex]
      \n[latex]\\begin{array}{rrlrrrr} 1&=&16x&+&20x&-&35 \\\\ +35&&&&&+&35 \\\\ \\hline \\dfrac{36}{36}&=&\\dfrac{36x}{36}&&&& \\\\ \\\\ x&=&1&&&& \\end{array}[\/latex]<\/li>\n
    17. [latex]\\left(-\\dfrac{11}{3}+\\dfrac{3b}{2}=\\dfrac{5b}{2}-\\dfrac{25}{6}\\right)(6)[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} -22&+&9b&=&15b&-&25 \\\\ +22&-&15b&&-15b&+&22 \\\\ \\hline &&\\dfrac{-6b}{-6}&=&\\dfrac{-3}{-6}&& \\\\ \\\\ &&b&=&\\dfrac{1}{2}&& \\end{array}[\/latex]<\/li>\n
    18. [latex]\\left(\\dfrac{7}{6}-\\dfrac{4n}{3}=-\\dfrac{3n}{2}+2n+3\\right)(6)[\/latex]
      \n[latex]\\begin{array}{rrrrlrrrr} 7&-&8n&=&-9n&+&12n&+&18 \\\\ -7&+&9n&&+9n&-&12n&-&7 \\\\ &-&12n&&&&&& \\\\ \\hline &&\\dfrac{-11n}{-11}&=&\\dfrac{11}{-11}&&&& \\\\ \\\\ &&n&=&-1&&&& \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":18,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1592","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1592","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1592\/revisions"}],"predecessor-version":[{"id":1593,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1592\/revisions\/1593"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1592\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1592"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1592"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1592"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}