{"id":2400,"date":"2019-10-09T14:37:37","date_gmt":"2019-10-09T18:37:37","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=2400"},"modified":"2019-10-10T13:01:28","modified_gmt":"2019-10-10T17:01:28","slug":"answer-key-2-4","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-2-4\/","title":{"raw":"Answer Key 2.4","rendered":"Answer Key 2.4"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{3}{5}\\left(1 + p\\right) = \\dfrac{21}{20}\\right)(20) \\\\ \\)\r\n\\(\\dfrac{3}{\\cancel{5}1}\\cdot \\cancel{20 }4(1 + p) = \\dfrac{21}{\\cancel{20}1}\\cdot \\cancel{20} \\\\ \\)\r\n\\(\\begin{array}{rrrrr}\r\n12&+&12p&=&\\phantom{-}21 \\\\\r\n-12&&&&-12 \\\\\r\n\\midrule\r\n&&\\dfrac{12p}{12}&=&\\dfrac{9}{12} \\\\ \\\\\r\n&&p&=&\\dfrac{3}{4}\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\phantom{1}\\)\r\n\\(\\left(-\\dfrac{1}{2} = \\dfrac{3k}{2} + \\dfrac{3}{2}\\right)(2) \\\\ \\)\r\n\\(\\begin{array}{rrrrr}\r\n-1&=&3k&+&3 \\\\\r\n-3&&&-&3 \\\\\r\n\\midrule\r\n\\dfrac{-4}{3}&=&\\dfrac{3k}{3}&& \\\\ \\\\\r\nk&=&-\\dfrac{4}{3}&&\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\phantom{1}\\)\r\n\\(\\left(0 = -\\dfrac{5}{4}x+\\dfrac{6}{4}\\right)(4) \\\\ \\)\r\n\\(\\begin{array}{rrlrr}\r\n0&=&-5x&+&6 \\\\\r\n+5x&&+5x&& \\\\\r\n\\midrule\r\n\\dfrac{5x}{5}&=&\\dfrac{6}{5}&& \\\\ \\\\\r\nx&=&\\dfrac{6}{5}&&\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{3n}{2} - 8 = -\\dfrac{29}{12}\\right)(12) \\\\ \\)\r\n\\(\\begin{array}{rrrrr}\r\n18n&-&96&=&-29 \\\\\r\n&+&96&&+96 \\\\\r\n\\midrule\r\n&&\\dfrac{18n}{18}&=&\\dfrac{67}{18} \\\\ \\\\\r\n&&n&=&\\dfrac{67}{18}\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{3}{4} - \\dfrac{5}{4}m = \\dfrac{108}{24}\\right)(24) \\\\ \\)\r\n\\(\\begin{array}{rrrrr}\r\n18&-&30m&=&108 \\\\\r\n-18&&&&-18 \\\\\r\n\\midrule\r\n&&\\dfrac{-30m}{-30}&=&\\dfrac{90}{-30} \\\\ \\\\\r\n&&m&=&-3\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{11}{4} + \\dfrac{3}{4}r = \\dfrac{160}{32}\\right)(32) \\\\ \\)\r\n\\(\\begin{array}{crcrr}\r\n11\\cdot 8&+&3r\\cdot 8&=&160 \\\\\r\n\\phantom{-}88&+&24r&=&160 \\\\\r\n-88&&&&-88 \\\\\r\n\\midrule\r\n&&\\dfrac{24r}{24}&=&\\dfrac{72}{24} \\\\ \\\\\r\n&&r&=&3\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\phantom{1}\\)\r\n\\(\\left(2b + \\dfrac{9}{5} = -\\dfrac{11}{5}\\right)(5) \\\\ \\)\r\n\\(\\begin{array}{rrrrr}\r\n10b&+&9&=&-11 \\\\\r\n&-&9&&-9 \\\\\r\n\\midrule\r\n&&\\dfrac{10b}{10}&=&\\dfrac{-20}{10} \\\\ \\\\\r\n&&b&=&-2\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{3}{2} - \\dfrac{7v}{4} = -\\dfrac{9}{8}\\right)(8) \\\\ \\)\r\n\\(\\begin{array}{rrrrr}\r\n3\\cdot 4&-&7r\\cdot 2&=&-9 \\\\\r\n\\phantom{-}12&-&14r&=&-9 \\\\\r\n-12&&&&-12 \\\\\r\n\\midrule\r\n&&\\dfrac{-14r}{-14}&=&\\dfrac{-21}{-14} \\\\ \\\\\r\n&&r&=&\\dfrac{3}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{21n}{6}+\\dfrac{3}{2} = \\dfrac{3}{2}\\right)(6) \\\\ \\)\r\n\\(\\begin{array}{rrrrr}\r\n\\dfrac{21n}{6}&+&3\\cdot 3&=&3\\cdot 3 \\\\\r\n&-&9&&-9 \\\\\r\n\\midrule\r\n&&\\dfrac{21n}{6}&=&0 \\\\ \\\\\r\n&&n&=&0\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{41}{9} = \\dfrac{5}{2}x+\\dfrac{10}{6} - \\dfrac{1}{3}x\\right)(18) \\\\ \\)\r\n\\(\\begin{array}{rrlrrrr}\r\n41\\cdot 2&=&5x\\cdot 9&+&10\\cdot 3&-&x\\cdot 6 \\\\\r\n82&=&45x&+&30&-&6x \\\\\r\n-30&&&-&30&& \\\\\r\n\\midrule\r\n\\dfrac{52}{39}&=&\\dfrac{39x}{39}&&&& \\\\ \\\\\r\nx&=&\\dfrac{4}{3}&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\phantom{1}\\)\r\n\\(\\left(-a + \\dfrac{40a}{12}-\\dfrac{5}{4}= -\\dfrac{19}{4}\\right)(12) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n-12a&+&40a&-&15&=&-57 \\\\\r\n&&&+&15&&+15 \\\\\r\n\\midrule\r\n&&&&\\dfrac{28a}{28}&=&\\dfrac{-42}{28} \\\\ \\\\\r\n&&&&a&=&-\\dfrac{3}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\phantom{1}\\)\r\n\\(\\left(-\\dfrac{7k}{12}+\\dfrac{1}{3}-\\dfrac{10k}{3}=-\\dfrac{13}{8} \\right)(24) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n-14k&+&8&-&80k&=&-39 \\\\\r\n&-&8&&&&-8 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-94k}{-94}&=&\\dfrac{-47}{-94} \\\\ \\\\\r\n&&&&k&=&\\dfrac{1}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{55}{6} = -\\dfrac{15p}{4}+\\dfrac{25}{6}\\right)(12) \\\\ \\)\r\n\\(\\begin{array}{rrlrr}\r\n110&=&-45p&+&50 \\\\\r\n-50&&&-&50 \\\\\r\n\\midrule\r\n\\dfrac{60}{-45}&=&\\dfrac{-45p}{-45}&& \\\\ \\\\\r\np&=&-\\dfrac{4}{3}&&\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\phantom{1}\\)\r\n\\(\\left(-\\dfrac{2x}{6}+\\dfrac{3}{8}-\\dfrac{7x}{2}=-\\dfrac{83}{24}\\right)(24) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n-8x&+&9&-&84x&=&-83 \\\\\r\n&-&9&&&&-9 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-92x}{-92}&=&\\dfrac{-92}{-92} \\\\ \\\\\r\n&&&&x&=&1\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\phantom{1}\\)\r\n\\(\\left(-\\dfrac{5}{8}=\\dfrac{5}{4}r-\\dfrac{15}{8}\\right)(8) \\\\ \\)\r\n\\(\\begin{array}{rrlrr}\r\n-5&=&10r&-&15 \\\\\r\n+15&&&+&15 \\\\\r\n\\midrule\r\n\\dfrac{10}{10}&=&\\dfrac{10r}{10}&& \\\\ \\\\\r\nr&=&1&&\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{1}{12}=\\dfrac{4x}{3}+\\dfrac{5x}{3}-\\dfrac{35}{12}\\right)(12) \\\\ \\)\r\n\\(\\begin{array}{rrlrrrr}\r\n1&=&16x&+&20x&-&35 \\\\\r\n+35&&&&&+&35 \\\\\r\n\\midrule\r\n\\dfrac{36}{36}&=&\\dfrac{36x}{36}&&&& \\\\ \\\\\r\nx&=&1&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\phantom{1}\\)\r\n\\(\\left(-\\dfrac{11}{3}+\\dfrac{3b}{2}=\\dfrac{5b}{2}-\\dfrac{25}{6}\\right)(6) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n-22&+&9b&=&15b&-&25 \\\\\r\n+22&-&15b&&-15b&+&22 \\\\\r\n\\midrule\r\n&&\\dfrac{-6b}{-6}&=&\\dfrac{-3}{-6}&& \\\\ \\\\\r\n&&b&=&\\dfrac{1}{2}&&\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{7}{6}-\\dfrac{4n}{3}=-\\dfrac{3n}{2}+2n+3\\right)(6) \\\\ \\)\r\n\\(\\begin{array}{rrrrlrrrr}\r\n7&-&8n&=&-9n&+&12n&+&18 \\\\\r\n-7&+&9n&&+9n&-&12n&-&7 \\\\\r\n&-&12n&&&&&& \\\\\r\n\\midrule\r\n&&\\dfrac{-11n}{-11}&=&\\dfrac{11}{-11}&&&& \\\\ \\\\\r\n&&n&=&-1&&&&\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\phantom{1}\"
      \n\"\left(\dfrac{3}{5}\left(1 + p\right) = \dfrac{21}{20}\right)(20) \\\"
      \n\"\dfrac{3}{\cancel{5}1}\cdot \cancel{20 }4(1 + p) = \dfrac{21}{\cancel{20}1}\cdot \cancel{20} \\\"
      \n\"\begin{array}{rrrrr}<\/li>\n
    2. \"\phantom{1}\"
      \n\"\left(-\dfrac{1}{2} = \dfrac{3k}{2} + \dfrac{3}{2}\right)(2) \\\"
      \n\"\begin{array}{rrrrr}<\/li>\n
    3. \"\phantom{1}\"
      \n\"\left(0 = -\dfrac{5}{4}x+\dfrac{6}{4}\right)(4) \\\"
      \n\"\begin{array}{rrlrr}<\/li>\n
    4. \"\phantom{1}\"
      \n\"\left(\dfrac{3n}{2} - 8 = -\dfrac{29}{12}\right)(12) \\\"
      \n\"\begin{array}{rrrrr}<\/li>\n
    5. \"\phantom{1}\"
      \n\"\left(\dfrac{3}{4} - \dfrac{5}{4}m = \dfrac{108}{24}\right)(24) \\\"
      \n\"\begin{array}{rrrrr}<\/li>\n
    6. \"\phantom{1}\"
      \n\"\left(\dfrac{11}{4} + \dfrac{3}{4}r = \dfrac{160}{32}\right)(32) \\\"
      \n\"\begin{array}{crcrr}<\/li>\n
    7. \"\phantom{1}\"
      \n\"\left(2b + \dfrac{9}{5} = -\dfrac{11}{5}\right)(5) \\\"
      \n\"\begin{array}{rrrrr}<\/li>\n
    8. \"\phantom{1}\"
      \n\"\left(\dfrac{3}{2} - \dfrac{7v}{4} = -\dfrac{9}{8}\right)(8) \\\"
      \n\"\begin{array}{rrrrr}<\/li>\n
    9. \"\phantom{1}\"
      \n\"\left(\dfrac{21n}{6}+\dfrac{3}{2} = \dfrac{3}{2}\right)(6) \\\"
      \n\"\begin{array}{rrrrr}<\/li>\n
    10. \"\phantom{1}\"
      \n\"\left(\dfrac{41}{9} = \dfrac{5}{2}x+\dfrac{10}{6} - \dfrac{1}{3}x\right)(18) \\\"
      \n\"\begin{array}{rrlrrrr}<\/li>\n
    11. \"\phantom{1}\"
      \n\"\left(-a + \dfrac{40a}{12}-\dfrac{5}{4}= -\dfrac{19}{4}\right)(12) \\\"
      \n\"\begin{array}{rrrrrrr}<\/li>\n
    12. \"\phantom{1}\"
      \n\"\left(-\dfrac{7k}{12}+\dfrac{1}{3}-\dfrac{10k}{3}=-\dfrac{13}{8} \right)(24) \\\"
      \n\"\begin{array}{rrrrrrr}<\/li>\n
    13. \"\phantom{1}\"
      \n\"\left(\dfrac{55}{6} = -\dfrac{15p}{4}+\dfrac{25}{6}\right)(12) \\\"
      \n\"\begin{array}{rrlrr}<\/li>\n
    14. \"\phantom{1}\"
      \n\"\left(-\dfrac{2x}{6}+\dfrac{3}{8}-\dfrac{7x}{2}=-\dfrac{83}{24}\right)(24) \\\"
      \n\"\begin{array}{rrrrrrr}<\/li>\n
    15. \"\phantom{1}\"
      \n\"\left(-\dfrac{5}{8}=\dfrac{5}{4}r-\dfrac{15}{8}\right)(8) \\\"
      \n\"\begin{array}{rrlrr}<\/li>\n
    16. \"\phantom{1}\"
      \n\"\left(\dfrac{1}{12}=\dfrac{4x}{3}+\dfrac{5x}{3}-\dfrac{35}{12}\right)(12) \\\"
      \n\"\begin{array}{rrlrrrr}<\/li>\n
    17. \"\phantom{1}\"
      \n\"\left(-\dfrac{11}{3}+\dfrac{3b}{2}=\dfrac{5b}{2}-\dfrac{25}{6}\right)(6) \\\"
      \n\"\begin{array}{rrrrrrr}<\/li>\n
    18. \"\phantom{1}\"
      \n\"\left(\dfrac{7}{6}-\dfrac{4n}{3}=-\dfrac{3n}{2}+2n+3\right)(6) \\\"
      \n\"\begin{array}{rrrrlrrrr}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":13,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-2400","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/2400","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":5,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/2400\/revisions"}],"predecessor-version":[{"id":2406,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/2400\/revisions\/2406"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/2400\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=2400"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=2400"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=2400"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=2400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}