{"id":1588,"date":"2021-12-02T19:38:38","date_gmt":"2021-12-03T00:38:38","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-2\/"},"modified":"2023-08-31T19:55:01","modified_gmt":"2023-08-31T23:55:01","slug":"answer-key-2-2","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-2\/","title":{"raw":"Answer Key 2.2","rendered":"Answer Key 2.2"},"content":{"raw":"
    \r\n \t
  1. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n5&+&\\dfrac{n}{4}&=&\\phantom{-}4 \\\\\r\n-5&&&&-5 \\\\\r\n\\hline\r\n&&4 \\left(\\dfrac{n}{4}\\right)&=&(-1)4 \\\\ \\\\\r\n&&n&=&-4\r\n\\end{array}[\/latex]<\/li>\r\n \t
  2. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrlrr}\r\n-2&=&-2m&+&12 \\\\\r\n-12&&&-&12 \\\\\r\n\\hline\r\n\\dfrac{-14}{-2}&=&\\dfrac{-2m}{-2}&& \\\\ \\\\\r\nm&=&7&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  3. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n102&=&-7r&+&4 \\\\\r\n-4&&&-&4 \\\\\r\n\\hline\r\n\\dfrac{98}{-7}&=&\\dfrac{-7r}{-7}&& \\\\ \\\\\r\nr&=&-14&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  4. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n27&=&21&-&3x \\\\\r\n-21&&-21&& \\\\\r\n\\hline\r\n\\dfrac{6}{-3}&=&\\dfrac{-3x}{-3}&& \\\\ \\\\\r\nx&=&-2&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  5. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n-8n&+&3&=&-77 \\\\\r\n&-&3&&-3 \\\\\r\n\\hline\r\n&&\\dfrac{-8n}{-8}&=&\\dfrac{-80}{-8} \\\\ \\\\\r\n&&n&=&10\r\n\\end{array}[\/latex]<\/li>\r\n \t
  6. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n-4&-&b&=&\\phantom{+}8 \\\\\r\n+4&&&&+4 \\\\\r\n\\hline\r\n&&(-b&=&\\phantom{-}12)(-1) \\\\\r\n&&b&=&-12\r\n\\end{array}[\/latex]<\/li>\r\n \t
  7. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\n\\dfrac{0}{-6}&=&\\dfrac{-6v}{-6} \\\\ \\\\\r\nv&=&0\r\n\\end{array}[\/latex]<\/li>\r\n \t
  8. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrl}\r\n-2&+&\\dfrac{x}{2}&=&\\phantom{+}4 \\\\\r\n+2&&&&+2 \\\\\r\n\\hline\r\n&&2\\left(\\dfrac{x}{2}\\right)&=&\\phantom{+}(6)2 \\\\ \\\\\r\n&&x&=&12\r\n\\end{array}[\/latex]<\/li>\r\n \t
  9. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrr}\r\n-8&=&\\dfrac{x}{5}&-&6 \\\\\r\n+6&&&+&6 \\\\\r\n\\hline\r\n5(-2)&=&\\left(\\dfrac{x}{5}\\right) 5&& \\\\ \\\\\r\nx&=&-10&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  10. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrr}\r\n-5&=&\\dfrac{a}{4}&-&1 \\\\\r\n+1&&&+&1 \\\\\r\n\\hline\r\n4(-4)&=&\\left(\\dfrac{a}{4}\\right) 4&& \\\\ \\\\\r\na&=&-16&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  11. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrcrr}\r\n0&=&-7&+&\\dfrac{k}{2} \\\\\r\n+7&&+7&& \\\\\r\n\\hline\r\n2(7)&=&\\left(\\dfrac{k}{2}\\right)2&& \\\\ \\\\\r\nk&=&14&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  12. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n-6&=&15&+&3p \\\\\r\n-15&&-15&& \\\\\r\n\\hline\r\n\\dfrac{-21}{3}&=&\\dfrac{3p}{3}&& \\\\ \\\\\r\np&=&-7&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  13. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrl}\r\n-12&+&3x&=&\\phantom{+1}0 \\\\\r\n+12&&&&+12 \\\\\r\n\\hline\r\n&&\\dfrac{3x}{3}&=&\\dfrac{12}{3} \\\\ \\\\\r\n&&x&=&4\r\n\\end{array}[\/latex]<\/li>\r\n \t
  14. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrr}\r\n-5m&+&2&=&27 \\\\\r\n&-&2&&-2 \\\\\r\n\\hline\r\n&&\\dfrac{-5m}{-5}&=&\\dfrac{25}{-5} \\\\ \\\\\r\n&&m&=&-5\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} 5&+&\\dfrac{n}{4}&=&\\phantom{-}4 \\\\ -5&&&&-5 \\\\ \\hline &&4 \\left(\\dfrac{n}{4}\\right)&=&(-1)4 \\\\ \\\\ &&n&=&-4 \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlrr} -2&=&-2m&+&12 \\\\ -12&&&-&12 \\\\ \\hline \\dfrac{-14}{-2}&=&\\dfrac{-2m}{-2}&& \\\\ \\\\ m&=&7&& \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 102&=&-7r&+&4 \\\\ -4&&&-&4 \\\\ \\hline \\dfrac{98}{-7}&=&\\dfrac{-7r}{-7}&& \\\\ \\\\ r&=&-14&& \\end{array}[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 27&=&21&-&3x \\\\ -21&&-21&& \\\\ \\hline \\dfrac{6}{-3}&=&\\dfrac{-3x}{-3}&& \\\\ \\\\ x&=&-2&& \\end{array}[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -8n&+&3&=&-77 \\\\ &-&3&&-3 \\\\ \\hline &&\\dfrac{-8n}{-8}&=&\\dfrac{-80}{-8} \\\\ \\\\ &&n&=&10 \\end{array}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} -4&-&b&=&\\phantom{+}8 \\\\ +4&&&&+4 \\\\ \\hline &&(-b&=&\\phantom{-}12)(-1) \\\\ &&b&=&-12 \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{0}{-6}&=&\\dfrac{-6v}{-6} \\\\ \\\\ v&=&0 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrl} -2&+&\\dfrac{x}{2}&=&\\phantom{+}4 \\\\ +2&&&&+2 \\\\ \\hline &&2\\left(\\dfrac{x}{2}\\right)&=&\\phantom{+}(6)2 \\\\ \\\\ &&x&=&12 \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrr} -8&=&\\dfrac{x}{5}&-&6 \\\\ +6&&&+&6 \\\\ \\hline 5(-2)&=&\\left(\\dfrac{x}{5}\\right) 5&& \\\\ \\\\ x&=&-10&& \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrr} -5&=&\\dfrac{a}{4}&-&1 \\\\ +1&&&+&1 \\\\ \\hline 4(-4)&=&\\left(\\dfrac{a}{4}\\right) 4&& \\\\ \\\\ a&=&-16&& \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrcrr} 0&=&-7&+&\\dfrac{k}{2} \\\\ +7&&+7&& \\\\ \\hline 2(7)&=&\\left(\\dfrac{k}{2}\\right)2&& \\\\ \\\\ k&=&14&& \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -6&=&15&+&3p \\\\ -15&&-15&& \\\\ \\hline \\dfrac{-21}{3}&=&\\dfrac{3p}{3}&& \\\\ \\\\ p&=&-7&& \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} -12&+&3x&=&\\phantom{+1}0 \\\\ +12&&&&+12 \\\\ \\hline &&\\dfrac{3x}{3}&=&\\dfrac{12}{3} \\\\ \\\\ &&x&=&4 \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -5m&+&2&=&27 \\\\ &-&2&&-2 \\\\ \\hline &&\\dfrac{-5m}{-5}&=&\\dfrac{25}{-5} \\\\ \\\\ &&m&=&-5 \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":16,"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-1588","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\/1588","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\/1588\/revisions"}],"predecessor-version":[{"id":2195,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1588\/revisions\/2195"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1588\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1588"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1588"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1588"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1588"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}