{"id":1594,"date":"2021-12-02T19:38:40","date_gmt":"2021-12-03T00:38:40","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-5\/"},"modified":"2022-11-02T10:36:49","modified_gmt":"2022-11-02T14:36:49","slug":"answer-key-2-5","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-5\/","title":{"raw":"Answer Key 2.5","rendered":"Answer Key 2.5"},"content":{"raw":"
    \n \t
  1. [latex]x=\\pm 8[\/latex]<\/li>\n \t
  2. [latex]n=\\pm 7[\/latex]<\/li>\n \t
  3. [latex]b=\\pm 1[\/latex]<\/li>\n \t
  4. [latex]x=\\pm 2[\/latex]<\/li>\n \t
  5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrr}\n5&+&8a&=&53 \\\\\n-5&&&&-5 \\\\\n\\hline\n&&\\dfrac{8a}{8}&=&\\dfrac{48}{8} \\\\ \\\\\n&&a&=&6\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrl}\n5&+&8a&=&-53 \\\\\n-5&&&&-5 \\\\\n\\hline\n&&\\dfrac{8a}{8}&=&\\dfrac{-58}{8} \\\\ \\\\\n&&a&=&-\\dfrac{58}{8}\\text{ or }-7\\dfrac{1}{4}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrl}\n9n&+&8&=&46 \\\\\n&-&8&&-8 \\\\\n\\hline\n&&\\dfrac{9n}{9}&=&\\dfrac{38}{9} \\\\ \\\\\n&&n&=&\\dfrac{38}{9}\\text{ or }4\\dfrac{2}{9}\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n9n&+&8&=&-46 \\\\\n&-&8&&-8 \\\\\n\\hline\n&&\\dfrac{9n}{9}&=&\\dfrac{-54}{9} \\\\ \\\\\n&&n&=&-6\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrr}\n3k&+&8&=&2 \\\\\n&-&8&&-8 \\\\\n\\hline\n&&\\dfrac{3k}{3}&=&\\dfrac{-6}{3} \\\\ \\\\\n&&k&=&-2\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n3k&+&8&=&-2 \\\\\n&-&8&&-8 \\\\\n\\hline\n&&\\dfrac{3k}{3}&=&\\dfrac{-10}{3} \\\\ \\\\\n&&k&=&-\\dfrac{10}{3}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrl}\n3&-&x&=&\\phantom{-}6 \\\\\n-3&&&&-3 \\\\\n\\hline\n&&(-x&=&\\phantom{-}3)(-1) \\\\\n&&x&=&-3\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrl}\n3&-&x&=&-6 \\\\\n-3&&&&-3 \\\\\n\\hline\n&&(-x&=&-9)(-1) \\\\\n&&x&=&\\phantom{-}9\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{-7}{-7}\\left| -3-3r \\right|&=&\\dfrac{-21}{-7} \\\\\n|-3-3r|&=&3\n\\end{array}[\/latex]\n[latex]\\phantom{1}[\/latex]\n[latex]\\begin{array}{ll}\n\\begin{array}{rrrrr}\n-3&-&3r&=&3 \\\\\n+3&&&&+3 \\\\\n\\hline\n&&\\dfrac{-3r}{-3}&=&\\dfrac{6}{-3} \\\\ \\\\\n&&r&=&-2\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}{rrrrr}\n-3&-&3r&=&-3 \\\\\n+3&&&&+3 \\\\\n\\hline\n&&\\dfrac{-3r}{-3}&=&\\dfrac{0}{-3} \\\\ \\\\\n&&r&=&0\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n|2+2b|&+&1&=&3 \\\\\n&-&1&&-1 \\\\\n\\hline\n|2+2b|&&&=&2 \\\\\n\\end{array}[\/latex]\n[latex]\\begin{array}[t]{ll} \\\\\n\\begin{array}[t]{rrrrr}\n2&+&2b&=&2 \\\\\n-2&&&&-2 \\\\\n\\hline\n&&2b&=&0 \\\\\n&&b&=&0\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n2&+&2b&=&-2 \\\\\n-2&&&&-2 \\\\\n\\hline\n&&\\dfrac{2b}{2}&=&\\dfrac{-4}{2} \\\\ \\\\\n&&b&=&-2\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{7}{7}|-7x-3|&=&\\dfrac{21}{7} \\\\\n|-7x-3|&=&3\n\\end{array}[\/latex]\n[latex]\\begin{array}[t]{ll}\\\\\n\\begin{array}[t]{rrrrr}\n-7x&-&3&=&3 \\\\\n&+&3&&+3 \\\\\n\\hline\n&&\\dfrac{-7x}{-7}&=&\\dfrac{6}{-7} \\\\ \\\\\n&&x&=&-\\dfrac{6}{7}\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n-7x&-&3&=&-3 \\\\\n&+&3&&+3 \\\\\n\\hline\n&&-7x&=&0 \\\\\n&&x&=&0\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrr}\n-4&-&3n&=&2 \\\\\n+4&&&&+4 \\\\\n\\hline\n&&\\dfrac{-3n}{-3}&=&\\dfrac{6}{-3} \\\\ \\\\\n&&n&=&-2\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n-4&-&3n&=&-2 \\\\\n+4&&&&+4 \\\\\n\\hline\n&&\\dfrac{-3n}{-3}&=&\\dfrac{2}{-3} \\\\ \\\\\n&&n&=&-\\dfrac{2}{3}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n8|5p &+&8|&-&5&=&11 \\\\\n&&&+&5&&+5 \\\\\n\\hline\n&&\\dfrac{8}{8}|5p &+&8|&=&\\dfrac{16}{8} \\\\\n&&|5p &+&8|&=&2\n\\end{array}[\/latex]\n[latex]\\begin{array}[t]{ll}\\\\\n\\begin{array}[t]{rrrrr}\n5p&+&8&=&2 \\\\\n&-&8&&-8 \\\\\n\\hline\n&&\\dfrac{5p}{5}&=&\\dfrac{-6}{5} \\\\ \\\\\n&&p&=&-\\dfrac{6}{5}\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n5p&+&8&=&-2 \\\\\n&-&8&&-8 \\\\\n\\hline\n&&\\dfrac{5p}{5}&=&\\dfrac{-10}{5} \\\\ \\\\\n&&p&=&-2\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n3&-&|6n&+&7|&=&-40 \\\\\n-3&&&&&&-3 \\\\\n\\hline\n&&(-|6n&+&7|&=&-43)(-1) \\\\\n&&|6n&+&7|&=&43\n\\end{array}[\/latex]\n[latex]\\begin{array}[t]{ll}\\\\\n\\begin{array}[t]{rrrrr}\n6n&+&7&=&43 \\\\\n&-&7&&-7 \\\\\n\\hline\n&&\\dfrac{6n}{6}&=&\\dfrac{36}{6} \\\\ \\\\\n&&n&=&6\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n6n&+&7&=&-43 \\\\\n&-&7&&-7 \\\\\n\\hline\n&&\\dfrac{6n}{6}&=&\\dfrac{-50}{6} \\\\ \\\\\n&&n&=&-\\dfrac{25}{3}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n5|3&+&7m|&+&1&=&51 \\\\\n&&&-&1&&-1 \\\\\n\\hline\n&&\\dfrac{5}{5}|3&+&7m|&=&\\dfrac{50}{5} \\\\\n&&|3&+&7m|&=&10\n\\end{array}[\/latex]\n[latex]\\begin{array}[t]{ll}\\\\\n\\begin{array}[t]{rrrrr}\n3&+&7m&=&10 \\\\\n-3&&&&-3 \\\\\n\\hline\n&&\\dfrac{7m}{7}&=&\\dfrac{7}{7} \\\\ \\\\\n&&m&=&1\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n3&+&7m&=&-10 \\\\\n-3&&&&-3 \\\\\n\\hline\n&&\\dfrac{7m}{7}&=&\\dfrac{-13}{7} \\\\ \\\\\n&&m&=&-\\dfrac{13}{7}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n4|r&+&7|&+&3&=&59 \\\\\n&&&-&3&&-3 \\\\\n\\hline\n&&\\dfrac{4}{4}|r&+&7|&=&\\dfrac{56}{4} \\\\\n&&|r&+&7|&=&14\n\\end{array}[\/latex]\n[latex]\\begin{array}[t]{ll}\\\\\n\\begin{array}[t]{rrrrr}\nr&+&7&=&14 \\\\\n&-&7&&-7 \\\\\n\\hline\n&&r&=&7\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\nr&+&7&=&-14 \\\\\n&-&7&&-7 \\\\\n\\hline\n&&r&=&-21\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n-7&+&8|-7x&-&3|&=&73 \\\\\n+7&&&&&&+7 \\\\\n\\hline\n&&\\dfrac{8}{8}|-7x&-&3|&=&\\dfrac{80}{8} \\\\\n&&|-7x&-&3|&=&10\n\\end{array}[\/latex]\n[latex]\\phantom{1}[\/latex]\n[latex]\\begin{array}{ll}\n\\begin{array}{rrrrr}\n-7x&-&3&=&10 \\\\\n&+&3&&+3 \\\\\n\\hline\n&&\\dfrac{-7x}{-7}&=&\\dfrac{13}{-7} \\\\ \\\\\n&&x&=&-\\dfrac{13}{7}\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}{rrrrr}\n-7x&-&3&=&-10 \\\\\n&+&3&&+3 \\\\\n\\hline\n&&\\dfrac{-7x}{-7}&=&\\dfrac{-7}{-7} \\\\ \\\\\n&&x&=&1\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n8|3&-&3n|&-&5&=&91 \\\\\n&&&+&5&&+5 \\\\\n\\hline\n&&\\dfrac{8}{8}|3&-&3n|&=&\\dfrac{96}{8} \\\\\n&&|3&-&3n|&=&12\n\\end{array}[\/latex]\n[latex]\\begin{array}[t]{ll}\\\\\n\\begin{array}[t]{rrrrr}\n3&-&3n&=&12 \\\\\n-3&&&&-3 \\\\\n\\hline\n&&\\dfrac{-3n}{-3}&=&\\dfrac{9}{-3} \\\\ \\\\\n&&n&=&-3\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrr}\n3&-&3n&=&-12 \\\\\n-3&&&&-3 \\\\\n\\hline\n&&\\dfrac{-3n}{-3}&=&\\dfrac{-15}{-3} \\\\ \\\\\n&&n&=&5\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  19. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrr}\n5x&+&3&=&2x&-&1 \\\\\n-2x&-&3&&-2x&-&3 \\\\\n\\hline\n&&\\dfrac{3x}{3}&=&\\dfrac{-4}{3}&& \\\\ \\\\\n&&x&=&-\\dfrac{4}{3}&&\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrrrr}\n5x&+&3&=&-2x&+&1 \\\\\n+2x&-&3&&+2x&-&3 \\\\\n\\hline\n&&\\dfrac{7x}{7}&=&\\dfrac{-2}{7}&& \\\\ \\\\\n&&x&=&-\\dfrac{2}{7}&&\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrr}\n2&+&3x&=&4&-&2x \\\\\n-2&+&2x&&-2&+&2x \\\\\n\\hline\n&&\\dfrac{5x}{5}&=&\\dfrac{2}{5}&& \\\\ \\\\\n&&x&=&\\dfrac{2}{5}&&\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrrrr}\n2&+&3x&=&-4&+&2x \\\\\n-2&-&2x&&-2&-&2x \\\\\n\\hline\n&&x&=&-6&&\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  21. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrr}\n3x&-&4&=&2x&+&3 \\\\\n-2x&+&4&&-2x&+&4 \\\\\n\\hline\n&&x&=&7&&\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrlrr}\n3x&-&4&=&-2x&-&3 \\\\\n+2x&+&4&&+2x&+&4 \\\\\n\\hline\n&&\\dfrac{5x}{5}&=&\\dfrac{1}{5}&& \\\\ \\\\\n&&x&=&\\dfrac{1}{5}&&\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  22. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrr}\n2x&-&5&=&3x&+&4 \\\\\n-3x&+&5&&-3x&+&5 \\\\\n\\hline\n&&-x&=&9&& \\\\\n&&x&=&-9&&\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrlrr}\n2x&-&5&=&-3x&-&4 \\\\\n+3x&+&5&&+3x&+&5 \\\\\n\\hline\n&&\\dfrac{5x}{5}&=&\\dfrac{1}{5}&& \\\\ \\\\\n&&x&=&\\dfrac{1}{5}&&\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  23. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrr}\n4x&-&2&=&6x&+&3 \\\\\n-6x&+&2&&-6x&+&2 \\\\\n\\hline\n&&\\dfrac{-2x}{-2}&=&\\dfrac{5}{-2}&& \\\\ \\\\\n&&x&=&-\\dfrac{5}{2}&&\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrrrr}\n4x&-&2&=&-6x&-&3 \\\\\n+6x&+&2&&+6x&+&2 \\\\\n\\hline\n&&\\dfrac{10x}{10}&=&\\dfrac{-1}{10}&& \\\\ \\\\\n&&x&=&-\\dfrac{1}{10}&&\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  24. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrr}\n3x&+&2&=&2x&-&3 \\\\\n-2x&-&2&&-2x&-&2 \\\\\n\\hline\n&&x&=&-5&&\n\\end{array}\n& \\hspace{0.5in}\n\\begin{array}[t]{rrrrlrr}\n3x&+&2&=&-2x&+&3 \\\\\n+2x&-&2&&+2x&-&2 \\\\\n\\hline\n&&\\dfrac{5x}{5}&=&\\dfrac{1}{5}&& \\\\ \\\\\n&&x&=&\\dfrac{1}{5}&&\n\\end{array}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]x=\\pm 8[\/latex]<\/li>\n
    2. [latex]n=\\pm 7[\/latex]<\/li>\n
    3. [latex]b=\\pm 1[\/latex]<\/li>\n
    4. [latex]x=\\pm 2[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrr} 5&+&8a&=&53 \\\\ -5&&&&-5 \\\\ \\hline &&\\dfrac{8a}{8}&=&\\dfrac{48}{8} \\\\ \\\\ &&a&=&6 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrl} 5&+&8a&=&-53 \\\\ -5&&&&-5 \\\\ \\hline &&\\dfrac{8a}{8}&=&\\dfrac{-58}{8} \\\\ \\\\ &&a&=&-\\dfrac{58}{8}\\text{ or }-7\\dfrac{1}{4} \\end{array} \\end{array}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrl} 9n&+&8&=&46 \\\\ &-&8&&-8 \\\\ \\hline &&\\dfrac{9n}{9}&=&\\dfrac{38}{9} \\\\ \\\\ &&n&=&\\dfrac{38}{9}\\text{ or }4\\dfrac{2}{9} \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} 9n&+&8&=&-46 \\\\ &-&8&&-8 \\\\ \\hline &&\\dfrac{9n}{9}&=&\\dfrac{-54}{9} \\\\ \\\\ &&n&=&-6 \\end{array} \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrr} 3k&+&8&=&2 \\\\ &-&8&&-8 \\\\ \\hline &&\\dfrac{3k}{3}&=&\\dfrac{-6}{3} \\\\ \\\\ &&k&=&-2 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} 3k&+&8&=&-2 \\\\ &-&8&&-8 \\\\ \\hline &&\\dfrac{3k}{3}&=&\\dfrac{-10}{3} \\\\ \\\\ &&k&=&-\\dfrac{10}{3} \\end{array} \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrl} 3&-&x&=&\\phantom{-}6 \\\\ -3&&&&-3 \\\\ \\hline &&(-x&=&\\phantom{-}3)(-1) \\\\ &&x&=&-3 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrl} 3&-&x&=&-6 \\\\ -3&&&&-3 \\\\ \\hline &&(-x&=&-9)(-1) \\\\ &&x&=&\\phantom{-}9 \\end{array} \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{-7}{-7}\\left| -3-3r \\right|&=&\\dfrac{-21}{-7} \\\\ |-3-3r|&=&3 \\end{array}[\/latex]
      \n[latex]\\phantom{1}[\/latex]
      \n[latex]\\begin{array}{ll} \\begin{array}{rrrrr} -3&-&3r&=&3 \\\\ +3&&&&+3 \\\\ \\hline &&\\dfrac{-3r}{-3}&=&\\dfrac{6}{-3} \\\\ \\\\ &&r&=&-2 \\end{array} & \\hspace{0.5in} \\begin{array}{rrrrr} -3&-&3r&=&-3 \\\\ +3&&&&+3 \\\\ \\hline &&\\dfrac{-3r}{-3}&=&\\dfrac{0}{-3} \\\\ \\\\ &&r&=&0 \\end{array} \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} |2+2b|&+&1&=&3 \\\\ &-&1&&-1 \\\\ \\hline |2+2b|&&&=&2 \\\\ \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\\\ \\begin{array}[t]{rrrrr} 2&+&2b&=&2 \\\\ -2&&&&-2 \\\\ \\hline &&2b&=&0 \\\\ &&b&=&0 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} 2&+&2b&=&-2 \\\\ -2&&&&-2 \\\\ \\hline &&\\dfrac{2b}{2}&=&\\dfrac{-4}{2} \\\\ \\\\ &&b&=&-2 \\end{array} \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{7}{7}|-7x-3|&=&\\dfrac{21}{7} \\\\ |-7x-3|&=&3 \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{ll}\\\\ \\begin{array}[t]{rrrrr} -7x&-&3&=&3 \\\\ &+&3&&+3 \\\\ \\hline &&\\dfrac{-7x}{-7}&=&\\dfrac{6}{-7} \\\\ \\\\ &&x&=&-\\dfrac{6}{7} \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} -7x&-&3&=&-3 \\\\ &+&3&&+3 \\\\ \\hline &&-7x&=&0 \\\\ &&x&=&0 \\end{array} \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrr} -4&-&3n&=&2 \\\\ +4&&&&+4 \\\\ \\hline &&\\dfrac{-3n}{-3}&=&\\dfrac{6}{-3} \\\\ \\\\ &&n&=&-2 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} -4&-&3n&=&-2 \\\\ +4&&&&+4 \\\\ \\hline &&\\dfrac{-3n}{-3}&=&\\dfrac{2}{-3} \\\\ \\\\ &&n&=&-\\dfrac{2}{3} \\end{array} \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 8|5p &+&8|&-&5&=&11 \\\\ &&&+&5&&+5 \\\\ \\hline &&\\dfrac{8}{8}|5p &+&8|&=&\\dfrac{16}{8} \\\\ &&|5p &+&8|&=&2 \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{ll}\\\\ \\begin{array}[t]{rrrrr} 5p&+&8&=&2 \\\\ &-&8&&-8 \\\\ \\hline &&\\dfrac{5p}{5}&=&\\dfrac{-6}{5} \\\\ \\\\ &&p&=&-\\dfrac{6}{5} \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} 5p&+&8&=&-2 \\\\ &-&8&&-8 \\\\ \\hline &&\\dfrac{5p}{5}&=&\\dfrac{-10}{5} \\\\ \\\\ &&p&=&-2 \\end{array} \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} 3&-&|6n&+&7|&=&-40 \\\\ -3&&&&&&-3 \\\\ \\hline &&(-|6n&+&7|&=&-43)(-1) \\\\ &&|6n&+&7|&=&43 \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{ll}\\\\ \\begin{array}[t]{rrrrr} 6n&+&7&=&43 \\\\ &-&7&&-7 \\\\ \\hline &&\\dfrac{6n}{6}&=&\\dfrac{36}{6} \\\\ \\\\ &&n&=&6 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} 6n&+&7&=&-43 \\\\ &-&7&&-7 \\\\ \\hline &&\\dfrac{6n}{6}&=&\\dfrac{-50}{6} \\\\ \\\\ &&n&=&-\\dfrac{25}{3} \\end{array} \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 5|3&+&7m|&+&1&=&51 \\\\ &&&-&1&&-1 \\\\ \\hline &&\\dfrac{5}{5}|3&+&7m|&=&\\dfrac{50}{5} \\\\ &&|3&+&7m|&=&10 \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{ll}\\\\ \\begin{array}[t]{rrrrr} 3&+&7m&=&10 \\\\ -3&&&&-3 \\\\ \\hline &&\\dfrac{7m}{7}&=&\\dfrac{7}{7} \\\\ \\\\ &&m&=&1 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} 3&+&7m&=&-10 \\\\ -3&&&&-3 \\\\ \\hline &&\\dfrac{7m}{7}&=&\\dfrac{-13}{7} \\\\ \\\\ &&m&=&-\\dfrac{13}{7} \\end{array} \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 4|r&+&7|&+&3&=&59 \\\\ &&&-&3&&-3 \\\\ \\hline &&\\dfrac{4}{4}|r&+&7|&=&\\dfrac{56}{4} \\\\ &&|r&+&7|&=&14 \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{ll}\\\\ \\begin{array}[t]{rrrrr} r&+&7&=&14 \\\\ &-&7&&-7 \\\\ \\hline &&r&=&7 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} r&+&7&=&-14 \\\\ &-&7&&-7 \\\\ \\hline &&r&=&-21 \\end{array} \\end{array}[\/latex]<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} -7&+&8|-7x&-&3|&=&73 \\\\ +7&&&&&&+7 \\\\ \\hline &&\\dfrac{8}{8}|-7x&-&3|&=&\\dfrac{80}{8} \\\\ &&|-7x&-&3|&=&10 \\end{array}[\/latex]
      \n[latex]\\phantom{1}[\/latex]
      \n[latex]\\begin{array}{ll} \\begin{array}{rrrrr} -7x&-&3&=&10 \\\\ &+&3&&+3 \\\\ \\hline &&\\dfrac{-7x}{-7}&=&\\dfrac{13}{-7} \\\\ \\\\ &&x&=&-\\dfrac{13}{7} \\end{array} & \\hspace{0.5in} \\begin{array}{rrrrr} -7x&-&3&=&-10 \\\\ &+&3&&+3 \\\\ \\hline &&\\dfrac{-7x}{-7}&=&\\dfrac{-7}{-7} \\\\ \\\\ &&x&=&1 \\end{array} \\end{array}[\/latex]<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 8|3&-&3n|&-&5&=&91 \\\\ &&&+&5&&+5 \\\\ \\hline &&\\dfrac{8}{8}|3&-&3n|&=&\\dfrac{96}{8} \\\\ &&|3&-&3n|&=&12 \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{ll}\\\\ \\begin{array}[t]{rrrrr} 3&-&3n&=&12 \\\\ -3&&&&-3 \\\\ \\hline &&\\dfrac{-3n}{-3}&=&\\dfrac{9}{-3} \\\\ \\\\ &&n&=&-3 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrr} 3&-&3n&=&-12 \\\\ -3&&&&-3 \\\\ \\hline &&\\dfrac{-3n}{-3}&=&\\dfrac{-15}{-3} \\\\ \\\\ &&n&=&5 \\end{array} \\end{array}[\/latex]<\/li>\n
    19. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrr} 5x&+&3&=&2x&-&1 \\\\ -2x&-&3&&-2x&-&3 \\\\ \\hline &&\\dfrac{3x}{3}&=&\\dfrac{-4}{3}&& \\\\ \\\\ &&x&=&-\\dfrac{4}{3}&& \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrrrr} 5x&+&3&=&-2x&+&1 \\\\ +2x&-&3&&+2x&-&3 \\\\ \\hline &&\\dfrac{7x}{7}&=&\\dfrac{-2}{7}&& \\\\ \\\\ &&x&=&-\\dfrac{2}{7}&& \\end{array} \\end{array}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrr} 2&+&3x&=&4&-&2x \\\\ -2&+&2x&&-2&+&2x \\\\ \\hline &&\\dfrac{5x}{5}&=&\\dfrac{2}{5}&& \\\\ \\\\ &&x&=&\\dfrac{2}{5}&& \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrrrr} 2&+&3x&=&-4&+&2x \\\\ -2&-&2x&&-2&-&2x \\\\ \\hline &&x&=&-6&& \\end{array} \\end{array}[\/latex]<\/li>\n
    21. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrr} 3x&-&4&=&2x&+&3 \\\\ -2x&+&4&&-2x&+&4 \\\\ \\hline &&x&=&7&& \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrlrr} 3x&-&4&=&-2x&-&3 \\\\ +2x&+&4&&+2x&+&4 \\\\ \\hline &&\\dfrac{5x}{5}&=&\\dfrac{1}{5}&& \\\\ \\\\ &&x&=&\\dfrac{1}{5}&& \\end{array} \\end{array}[\/latex]<\/li>\n
    22. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrr} 2x&-&5&=&3x&+&4 \\\\ -3x&+&5&&-3x&+&5 \\\\ \\hline &&-x&=&9&& \\\\ &&x&=&-9&& \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrlrr} 2x&-&5&=&-3x&-&4 \\\\ +3x&+&5&&+3x&+&5 \\\\ \\hline &&\\dfrac{5x}{5}&=&\\dfrac{1}{5}&& \\\\ \\\\ &&x&=&\\dfrac{1}{5}&& \\end{array} \\end{array}[\/latex]<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrr} 4x&-&2&=&6x&+&3 \\\\ -6x&+&2&&-6x&+&2 \\\\ \\hline &&\\dfrac{-2x}{-2}&=&\\dfrac{5}{-2}&& \\\\ \\\\ &&x&=&-\\dfrac{5}{2}&& \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrrrr} 4x&-&2&=&-6x&-&3 \\\\ +6x&+&2&&+6x&+&2 \\\\ \\hline &&\\dfrac{10x}{10}&=&\\dfrac{-1}{10}&& \\\\ \\\\ &&x&=&-\\dfrac{1}{10}&& \\end{array} \\end{array}[\/latex]<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrr} 3x&+&2&=&2x&-&3 \\\\ -2x&-&2&&-2x&-&2 \\\\ \\hline &&x&=&-5&& \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrrrlrr} 3x&+&2&=&-2x&+&3 \\\\ +2x&-&2&&+2x&-&2 \\\\ \\hline &&\\dfrac{5x}{5}&=&\\dfrac{1}{5}&& \\\\ \\\\ &&x&=&\\dfrac{1}{5}&& \\end{array} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":19,"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-1594","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\/1594","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\/1594\/revisions"}],"predecessor-version":[{"id":1595,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1594\/revisions\/1595"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1594\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1594"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1594"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1594"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1594"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}