{"id":1586,"date":"2021-12-02T19:38:38","date_gmt":"2021-12-03T00:38:38","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-1\/"},"modified":"2023-08-31T19:54:09","modified_gmt":"2023-08-31T23:54:09","slug":"answer-key-2-1","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-1\/","title":{"raw":"Answer Key 2.1","rendered":"Answer Key 2.1"},"content":{"raw":"
    \r\n \t
  1. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nv+9&=&16 \\\\\r\n-9&&-9 \\\\\r\n\\hline\r\nv&=&7\r\n\\end{array}[\/latex]<\/li>\r\n \t
  2. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n14&=&b&+&3 \\\\\r\n-3&&&-&3 \\\\\r\n\\hline\r\n11&=&b&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  3. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\nx&-&11&=&-16 \\\\\r\n&+&11&&+11 \\\\\r\n\\hline\r\n&&x&=&-5\r\n\\end{array}[\/latex]<\/li>\r\n \t
  4. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n-14&=&x&-&18 \\\\\r\n+18&&&+&18 \\\\\r\n\\hline\r\nx&=&4&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  5. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n30&=&a&+&20 \\\\\r\n-20&&&-&20 \\\\\r\n\\hline\r\na&=&10&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  6. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n-1&+&k&=&5 \\\\\r\n+1&&&&+1 \\\\\r\n\\hline\r\n&&k&=&6\r\n\\end{array}[\/latex]<\/li>\r\n \t
  7. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\nx&-&7&=&-26 \\\\\r\n&+&7&&+7 \\\\\r\n\\hline\r\n&&x&=&-19\r\n\\end{array}[\/latex]<\/li>\r\n \t
  8. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n-13&+&p&=&-19 \\\\\r\n+13&&&&+13 \\\\\r\n\\hline\r\n&&p&=&-6\r\n\\end{array}[\/latex]<\/li>\r\n \t
  9. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n13&=&n&-&5 \\\\\r\n+5&&&+&5 \\\\\r\n\\hline\r\nn&=&18&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  10. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n22&=&16&+&m \\\\\r\n-16&&-16&& \\\\\r\n\\hline\r\nm&=&6&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  11. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{340}{-17}&=&\\dfrac{-17x}{-17} \\\\ \\\\\r\nx&=&-20\r\n\\end{array}[\/latex]<\/li>\r\n \t
  12. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{4r}{4}&=&\\dfrac{-28}{4} \\\\ \\\\\r\nr&=&-7\r\n\\end{array}[\/latex]<\/li>\r\n \t
  13. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n\\left(-9=\\dfrac{n}{12}\\right)(12) \\\\ \\\\\r\nn=-108\r\n\\end{array}[\/latex]<\/li>\r\n \t
  14. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{27}{9}&=&\\dfrac{9b}{9} \\\\ \\\\\r\nb&=&3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  15. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{20v}{20}&=&\\dfrac{-160}{20} \\\\ \\\\\r\nv&=&-8\r\n\\end{array}[\/latex]<\/li>\r\n \t
  16. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{-20x}{-20}&=&\\dfrac{-80}{-20} \\\\ \\\\\r\nx&=&4\r\n\\end{array}[\/latex]<\/li>\r\n \t
  17. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{340}{20}&=&\\dfrac{20n}{20} \\\\ \\\\\r\nn&=&17\r\n\\end{array}[\/latex]<\/li>\r\n \t
  18. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{12}{8}&=&\\dfrac{8a}{8} \\\\ \\\\\r\na&=&\\dfrac{3}{2}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  19. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{16x}{16}&=&\\dfrac{320}{16} \\\\ \\\\\r\nx&=&20\r\n\\end{array}[\/latex]<\/li>\r\n \t
  20. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{8k}{8}&=&\\dfrac{-16}{8} \\\\ \\\\\r\nk&=&-2\r\n\\end{array}[\/latex]<\/li>\r\n \t
  21. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n-16&+&n&=&-13 \\\\\r\n+16&&&&+16 \\\\\r\n\\hline\r\n&&n&=&3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  22. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n-21&=&x&-&5 \\\\\r\n+5&&&+&5 \\\\\r\n\\hline\r\nx&=&-16&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  23. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\np&-&8&=&-21 \\\\\r\n&+&8&&+8 \\\\\r\n\\hline\r\n&&p&=&-13\r\n\\end{array}[\/latex]<\/li>\r\n \t
  24. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\nm&-&4&=&-13 \\\\\r\n&+&4&&+4 \\\\\r\n\\hline\r\n&&m&=&-9\r\n\\end{array}[\/latex]<\/li>\r\n \t
  25. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n\\left(\\dfrac{r}{14}=\\dfrac{5}{14}\\right)(14) \\\\ \\\\\r\nr=5\r\n\\end{array}[\/latex]<\/li>\r\n \t
  26. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n\\left(\\dfrac{n}{8}=40\\right)(8) \\\\ \\\\\r\nn=320\r\n\\end{array}[\/latex]<\/li>\r\n \t
  27. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{20b}{20}&=&\\dfrac{-200}{20} \\\\ \\\\\r\nb&=&-10\r\n\\end{array}[\/latex]<\/li>\r\n \t
  28. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n\\left(-\\dfrac{1}{3}=\\dfrac{x}{12}\\right) (12) \\\\ \\\\\r\n-\\dfrac{1}{3}\\cdot 12 = x \\\\\r\n\\phantom{-\\dfrac{1}{3}\\cdot 1}x=-4\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} v+9&=&16 \\\\ -9&&-9 \\\\ \\hline v&=&7 \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 14&=&b&+&3 \\\\ -3&&&-&3 \\\\ \\hline 11&=&b&& \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} x&-&11&=&-16 \\\\ &+&11&&+11 \\\\ \\hline &&x&=&-5 \\end{array}[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -14&=&x&-&18 \\\\ +18&&&+&18 \\\\ \\hline x&=&4&& \\end{array}[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 30&=&a&+&20 \\\\ -20&&&-&20 \\\\ \\hline a&=&10&& \\end{array}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -1&+&k&=&5 \\\\ +1&&&&+1 \\\\ \\hline &&k&=&6 \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} x&-&7&=&-26 \\\\ &+&7&&+7 \\\\ \\hline &&x&=&-19 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -13&+&p&=&-19 \\\\ +13&&&&+13 \\\\ \\hline &&p&=&-6 \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 13&=&n&-&5 \\\\ +5&&&+&5 \\\\ \\hline n&=&18&& \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 22&=&16&+&m \\\\ -16&&-16&& \\\\ \\hline m&=&6&& \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{340}{-17}&=&\\dfrac{-17x}{-17} \\\\ \\\\ x&=&-20 \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{4r}{4}&=&\\dfrac{-28}{4} \\\\ \\\\ r&=&-7 \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{l} \\left(-9=\\dfrac{n}{12}\\right)(12) \\\\ \\\\ n=-108 \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{27}{9}&=&\\dfrac{9b}{9} \\\\ \\\\ b&=&3 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{20v}{20}&=&\\dfrac{-160}{20} \\\\ \\\\ v&=&-8 \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{-20x}{-20}&=&\\dfrac{-80}{-20} \\\\ \\\\ x&=&4 \\end{array}[\/latex]<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{340}{20}&=&\\dfrac{20n}{20} \\\\ \\\\ n&=&17 \\end{array}[\/latex]<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{12}{8}&=&\\dfrac{8a}{8} \\\\ \\\\ a&=&\\dfrac{3}{2} \\end{array}[\/latex]<\/li>\n
    19. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{16x}{16}&=&\\dfrac{320}{16} \\\\ \\\\ x&=&20 \\end{array}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{8k}{8}&=&\\dfrac{-16}{8} \\\\ \\\\ k&=&-2 \\end{array}[\/latex]<\/li>\n
    21. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -16&+&n&=&-13 \\\\ +16&&&&+16 \\\\ \\hline &&n&=&3 \\end{array}[\/latex]<\/li>\n
    22. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -21&=&x&-&5 \\\\ +5&&&+&5 \\\\ \\hline x&=&-16&& \\end{array}[\/latex]<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} p&-&8&=&-21 \\\\ &+&8&&+8 \\\\ \\hline &&p&=&-13 \\end{array}[\/latex]<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} m&-&4&=&-13 \\\\ &+&4&&+4 \\\\ \\hline &&m&=&-9 \\end{array}[\/latex]<\/li>\n
    25. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{l} \\left(\\dfrac{r}{14}=\\dfrac{5}{14}\\right)(14) \\\\ \\\\ r=5 \\end{array}[\/latex]<\/li>\n
    26. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{l} \\left(\\dfrac{n}{8}=40\\right)(8) \\\\ \\\\ n=320 \\end{array}[\/latex]<\/li>\n
    27. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{20b}{20}&=&\\dfrac{-200}{20} \\\\ \\\\ b&=&-10 \\end{array}[\/latex]<\/li>\n
    28. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{l} \\left(-\\dfrac{1}{3}=\\dfrac{x}{12}\\right) (12) \\\\ \\\\ -\\dfrac{1}{3}\\cdot 12 = x \\\\ \\phantom{-\\dfrac{1}{3}\\cdot 1}x=-4 \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":15,"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-1586","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\/1586","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":3,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1586\/revisions"}],"predecessor-version":[{"id":2193,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1586\/revisions\/2193"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1586\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1586"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1586"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1586"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1586"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}