{"id":1357,"date":"2019-06-18T14:09:55","date_gmt":"2019-06-18T18:09:55","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1357"},"modified":"2020-02-03T14:43:00","modified_gmt":"2020-02-03T19:43:00","slug":"answer-key-4-1","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-4-1\/","title":{"raw":"Answer Key 4.1","rendered":"Answer Key 4.1"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\((-5, \\infty)\\)\u00a0 \u00a0 \u00a0\"-5,<\/li>\r\n \t
  2. \\((4, \\infty)\\)\u00a0 \u00a0 \u00a0 \u00a0\"4,<\/li>\r\n \t
  3. \\((-2, \\infty)\\)\u00a0 \u00a0\"-2,<\/li>\r\n \t
  4. \\((-\\infty, 1]\\)\u00a0 \u00a0 \u00a0\"-<\/li>\r\n \t
  5. \\((-\\infty, 5]\\)\u00a0 \u00a0\u00a0\"-<\/li>\r\n \t
  6. \\((-5, \\infty)\\)\u00a0 \u00a0 \u00a0\"-5,<\/li>\r\n \t
  7. \\(x>-5\\hspace{0.25in} (-5, \\infty)\\)\u00a0 \u00a0 \u00a0\"x<\/li>\r\n \t
  8. \\(x>0\\hspace{0.25in} (0, \\infty)\\)\u00a0 \u00a0 \u00a0 \u00a0\u00a0\"(x<\/li>\r\n \t
  9. \\(x\\ge -3 \\hspace{0.25in} [-3, \\infty)\\)\u00a0 \u00a0 \u00a0\"x<\/li>\r\n \t
  10. \\(x\\le 6 \\hspace{0.25in} (-\\infty, 6]\\)\u00a0 \u00a0 \u00a0\"x<\/li>\r\n \t
  11. \\(x\\le -1 \\hspace{0.25in} (-\\infty, -1]\\)\u00a0 \u00a0 \u00a0\"x<\/li>\r\n \t
  12. \\(x < 6 \\hspace{0.25in} (-\\infty, 6)\\)\u00a0 \u00a0 \u00a0\u00a0\"x<\/li>\r\n \t
  13. \\(\\begin{array}{rrrl}\r\n\\\\ \\\\\r\n(\\dfrac{x}{11}&\\ge &10)&(11) \\\\ \\\\\r\nx& \\ge & 110 &\r\n\\end{array}\\)\\(\\text{Interval notation: } [110,\\infty)\\)\u00a0\u00a0\"Number<\/li>\r\n \t
  14. \\(\\begin{array}{rrrl}\r\n\\\\ \\\\\r\n(-2 &\\le & \\dfrac{n}{13})&(13) \\\\ \\\\\r\n-26& \\le & n &\r\n\\end{array}\\)\\(\\text{Interval notation: } [-26, \\infty)\\)\u00a0\"Number<\/li>\r\n \t
  15. \\(\\begin{array}{rrrlr}\r\n\\\\ \\\\\r\n2 &+ & r&<&3 \\\\\r\n-2&&&& -2 \\\\\r\n\\midrule\r\n&&r&<&1\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, 1)\\)\u00a0\"Number<\/li>\r\n \t
  16. \\(\\begin{array}{rrrl}\r\n\\\\ \\\\\r\n(\\dfrac{m}{5} &\\le & -\\dfrac{6}{5})&(5) \\\\ \\\\\r\nm& \\le & -6 &\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, -6]\\)\u00a0\"Number<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n8&+&\\dfrac{n}{3}&\\ge & 6 & \\\\\r\n-8&&&&-8 & \\\\\r\n\\midrule\r\n&&(\\dfrac{n}{3} &\\ge & -2)& (3) \\\\ \\\\\r\n&&n & \\ge & -6 &\r\n\\end{array}\\)\\(\\text{Interval notation: } [-6, \\infty)\\)\u00a0\"Number<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n11&>&8&+ & \\dfrac{x}{2} \\\\\r\n-8&&-8&& \\\\\r\n\\midrule\r\n(3 &> & \\dfrac{x}{2})& (2)& \\\\ \\\\\r\n6 & > & x &&\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, 6)\\)\u00a0\"Number<\/li>\r\n \t
  19. \\(\\left(2>\\dfrac{(a-2)}{5}\\right)(5)\\)\\(\\begin{array}{rrrrr}\r\n10&>&a&-&2 \\\\\r\n+2&&&+&2 \\\\\r\n\\midrule\r\n12&>&a&&\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, 12)\\)\u00a0\"Number<\/li>\r\n \t
  20. \\(\\left(\\dfrac{(v-9)}{-4}\\le 2 \\right)(-4)\\)\\(\\begin{array}{rrrrr}\r\nv&-&9&\\ge &-8 \\\\\r\n&+&9&&+9 \\\\\r\n\\midrule\r\n&&v&\\ge &1\r\n\\end{array}\\)\\(\\text{Interval notation: } [1, \\infty)\\)\u00a0\u00a0\"Number<\/li>\r\n \t
  21. \\(\\begin{array}{rrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-47&\\ge &8&-& 5x \\\\\r\n-8&&-8&& \\\\\r\n\\midrule\r\n\\dfrac{-55}{-5}&\\ge &\\dfrac{-5x}{-5} && \\\\ \\\\\r\n11& \\le & x &&\r\n\\end{array}\\)\\(\\text{Interval notation: } [11, \\infty)\\)\u00a0\u00a0\"Number<\/li>\r\n \t
  22. \\(\\left(\\dfrac{(6+x)}{12}\\le -1 \\right)(12)\\)\\(\\begin{array}{rrrrr}\r\n6&+&x&\\le &-12 \\\\\r\n-6&&&&-6 \\\\\r\n\\midrule\r\n&&x&\\le &-18\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, -18]\\)\u00a0\"Number<\/li>\r\n \t
  23. \\(\\begin{array}{rrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{-2}{-2}(3&+ &k)&<& \\dfrac{-44}{-2} \\\\ \\\\\r\n3&+ &k &>&22 \\\\\r\n-3&&&&-3 \\\\\r\n\\midrule\r\n&& k&>&19\r\n\\end{array}\\)\\(\\text{Interval notation: } (19, \\infty)\\)\u00a0\"Number<\/li>\r\n \t
  24. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-7n&- &10&\\ge &60 \\\\\r\n&+&10&&+10 \\\\\r\n\\midrule\r\n&&\\dfrac{-7n}{-7}&\\ge & \\dfrac{70}{-7} \\\\ \\\\\r\n&&n&\\le &-10\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, -10]\\)\u00a0\"Number<\/li>\r\n \t
  25. \\(\\begin{array}{rrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{18}{-2}&<&\\dfrac{-2}{-2}(-8&+&p) \\\\ \\\\\r\n-9&>&-8&+&p \\\\\r\n+8&&+8&& \\\\\r\n\\midrule\r\n-1&>&p&&\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, -1)\\)\u00a0\u00a0\"Number<\/li>\r\n \t
  26. \\(\\left(5> \\dfrac{x}{5}+1 \\right)(5)\\)\\(\\begin{array}{rrrrr}\r\n25&\\ge &x&+ &5 \\\\\r\n-5&&&&-5 \\\\\r\n\\midrule\r\n20&\\ge &x& &\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, 20]\\)\u00a0\u00a0\"Number<\/li>\r\n \t
  27. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{24}{-6}&\\ge &\\dfrac{-6}{-6}(m&-&6) \\\\ \\\\\r\n-4&\\le &m&-&6 \\\\\r\n+6&&&+&6 \\\\\r\n\\midrule\r\n2&\\le &m&&\r\n\\end{array}\\)\\(\\text{Interval notation: } [2, \\infty)\\)\u00a0\"\"<\/li>\r\n \t
  28. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{-8}{-8}(n&-&5)&\\ge &\\dfrac{0}{-8} \\\\ \\\\\r\nn&-&5&\\le &0 \\\\\r\n&+&5&&+5 \\\\\r\n\\midrule\r\n&&n&\\le &5\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, 5]\\)\u00a0\"\"<\/li>\r\n \t
  29. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-r&-&5(r&-&6)&<&-18 \\\\\r\n-r&-&5r&+&30&<&-18 \\\\\r\n&&&-&30&&-30 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-6r}{-6}&<&\\dfrac{-48}{-6} \\\\ \\\\\r\n&&&&r&>&8 \\\\\r\n\\end{array}\\)\\(\\text{Interval notation: } (8, \\infty)\\)\u00a0\"\"<\/li>\r\n \t
  30. \\(\\begin{array}{rrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{-60}{-4}&\\ge &\\dfrac{-4}{-4}(-6x&-&3) \\\\ \\\\\r\n15&\\le &-6x&-&3 \\\\\r\n+3&&&+&3 \\\\\r\n\\midrule\r\n\\dfrac{18}{-6}&\\le&\\dfrac{-6x}{-6}&& \\\\ \\\\\r\n-3&\\ge &x &&\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, -3]\\)\u00a0\"Number<\/li>\r\n \t
  31. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\dfrac{24+4b}{4}&<&\\dfrac{4}{4}(1&+&6b) \\\\ \\\\\r\n6&+&b&<&1&+&6b \\\\\r\n-1&-&b&&-1&-&b \\\\\r\n\\midrule\r\n&&\\dfrac{5}{5}&<&\\dfrac{5b}{5}&& \\\\ \\\\\r\n&&b&>&1&&\r\n\\end{array}\\)\\(\\text{Interval notation: } (1, \\infty)\\)\u00a0\"Number<\/li>\r\n \t
  32. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\\r\n-8(2&-&2n)&\\ge &-16&+&n \\\\\r\n-16&+&16n& \\ge & -16 & + & n\\\\\r\n+16&-&n&&+16 &-& n\\\\\r\n\\midrule\r\n&&15n& \\ge &0 &&\\\\\r\n&&n& \\ge &0 &&\\\\\r\n\\end{array}\\)\\(\\text{Interval notation: } [0, \\infty)\\)\u00a0\"Number<\/li>\r\n \t
  33. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\dfrac{-5v-5}{-5}&<&\\dfrac{-5}{-5}(4v&+&1) \\\\ \\\\\r\nv&+&1&>&4v&+&1 \\\\\r\n-v&-&1&&-v&-&1 \\\\\r\n\\midrule\r\n&&\\dfrac{0}{3}&>&\\dfrac{3v}{3}&& \\\\ \\\\\r\n&&v&<&0&&\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, 0)\\)\u00a0\"Number<\/li>\r\n \t
  34. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-36&+&6x&>&-8(x&+&2)&+&4x \\\\\r\n-36&+&6x&>&-8x&-&16&+&4x \\\\\r\n+16&-&6x&&-6x&+&16&& \\\\\r\n\\midrule\r\n&&\\dfrac{-20}{-10}&>&\\dfrac{-10x}{-10}&&&& \\\\ \\\\\r\n&&x&>&2&&&& \\\\\r\n\\end{array}\\)\\(\\text{Interval notation: } (2, \\infty)\\)\u00a0\"Number<\/li>\r\n \t
  35. \\(\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n4&+&2(a&+&5)&<&-2(-a&-&4) \\\\\r\n4&+&2a&+&10&<&2a&+&8 \\\\\r\n-4&-&2a&-&10&&-2a&-&10-4 \\\\\r\n\\midrule\r\n&&0&<&-6&&&&\r\n\\end{array}\\)\\(\\text{False. No solution.}\\)\u00a0\"Number<\/li>\r\n \t
  36. \\(\\begin{array}{rrrrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n3(n&+&3)&+&7(8&-&8n)&<&5n&+&5&+&2 \\\\\r\n3n&+&9&+&56&-&56n&<&5n&+&7&& \\\\\r\n&&&&-53n&+&65&<&5n&+&7&& \\\\\r\n&&&&-5n&-&65&&-5n&-&65&& \\\\\r\n\\midrule\r\n&&&&&&-58n&<&-58&&&& \\\\\r\n&&&&&&n&>&1&&&& \\\\\r\n\\end{array}\\)\\(\\text{Interval notation: } (1, \\infty)\\)\r\n\"\"<\/li>\r\n \t
  37. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\\r\n-(k&-&2)&>&-k&-&20 \\\\\r\n-k&+&2&>&-k&-&20 \\\\\r\n+k&-&2&&+k&-&2 \\\\\r\n\\midrule\r\n&&0&>&-22&& \\\\\r\n\\end{array}\\)\\(\\text{Always true. Solution is all real numbers:} (-\\infty, \\infty)\\)\u00a0\"Number<\/li>\r\n \t
  38. \\(\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n-(4&-&5p)&+&3&\\ge &-2(8&-&5p) \\\\\r\n-4&+&5p&+&3&\\ge &-16&+&10p \\\\\r\n&&-1&+&5p&\\ge &-16&+&10p \\\\\r\n&&+1&-&10p&&+1&-&10p \\\\\r\n\\midrule\r\n&&&&\\dfrac{-5p}{-5}&\\ge &\\dfrac{-15}{-5}&& \\\\ \\\\\r\n&&&&p&\\le &3&& \\\\\r\n\\end{array}\\)\\(\\text{Interval notation: } (-\\infty, 3]\\)\u00a0\"Number<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"(-5, \infty)\"\u00a0 \u00a0 \u00a0\"-5,<\/li>\n
    2. \"(4, \infty)\"\u00a0 \u00a0 \u00a0 \u00a0\"4,<\/li>\n
    3. \"(-2, \infty)\"\u00a0 \u00a0\"-2,<\/li>\n
    4. \"(-\infty, 1]\"\u00a0 \u00a0 \u00a0\"-<\/li>\n
    5. \"(-\infty, 5]\"\u00a0 \u00a0\u00a0\"-<\/li>\n
    6. \"(-5, \infty)\"\u00a0 \u00a0 \u00a0\"-5,<\/li>\n
    7. \"x>-5\hspace{0.25in} (-5, \infty)\"\u00a0 \u00a0 \u00a0\"x<\/li>\n
    8. \"x>0\hspace{0.25in} (0, \infty)\"\u00a0 \u00a0 \u00a0 \u00a0\u00a0\"(x<\/li>\n
    9. \"x\ge -3 \hspace{0.25in} [-3, \infty)\"\u00a0 \u00a0 \u00a0\"x<\/li>\n
    10. \"x\le 6 \hspace{0.25in} (-\infty, 6]\"\u00a0 \u00a0 \u00a0\"x<\/li>\n
    11. \"x\le -1 \hspace{0.25in} (-\infty, -1]\"\u00a0 \u00a0 \u00a0\"x<\/li>\n
    12. \"x < 6 \hspace{0.25in} (-\infty, 6)\"\u00a0 \u00a0 \u00a0\u00a0\"x<\/li>\n
    13. \"\begin{array}{rrrl}\"\text{Interval notation: } [110,\infty)\"\u00a0\u00a0\"Number<\/li>\n
    14. \"\begin{array}{rrrl}\"\text{Interval notation: } [-26, \infty)\"\u00a0\"Number<\/li>\n
    15. \"\begin{array}{rrrlr}\"\text{Interval notation: } (-\infty, 1)\"\u00a0\"Number<\/li>\n
    16. \"\begin{array}{rrrl}\"\text{Interval notation: } (-\infty, -6]\"\u00a0\"Number<\/li>\n
    17. \"\begin{array}{rrrrrr}\"\text{Interval notation: } [-6, \infty)\"\u00a0\"Number<\/li>\n
    18. \"\begin{array}{rrrrr}\"\text{Interval notation: } (-\infty, 6)\"\u00a0\"Number<\/li>\n
    19. \"\left(2>\dfrac{(a-2)}{5}\right)(5)\"\"\begin{array}{rrrrr}\"\text{Interval notation: } (-\infty, 12)\"\u00a0\"Number<\/li>\n
    20. \"\left(\dfrac{(v-9)}{-4}\le 2 \right)(-4)\"\"\begin{array}{rrrrr}\"\text{Interval notation: } [1, \infty)\"\u00a0\u00a0\"Number<\/li>\n
    21. \"\begin{array}{rrrrl}\"\text{Interval notation: } [11, \infty)\"\u00a0\u00a0\"Number<\/li>\n
    22. \"\left(\dfrac{(6+x)}{12}\le -1 \right)(12)\"\"\begin{array}{rrrrr}\"\text{Interval notation: } (-\infty, -18]\"\u00a0\"Number<\/li>\n
    23. \"\begin{array}{rrrrl}\"\text{Interval notation: } (19, \infty)\"\u00a0\"Number<\/li>\n
    24. \"\begin{array}{rrrrr}\"\text{Interval notation: } (-\infty, -10]\"\u00a0\"Number<\/li>\n
    25. \"\begin{array}{rrrrl}\"\text{Interval notation: } (-\infty, -1)\"\u00a0\u00a0\"Number<\/li>\n
    26. \"\left(5> \dfrac{x}{5}+1 \right)(5)\"\"\begin{array}{rrrrr}\"\text{Interval notation: } (-\infty, 20]\"\u00a0\u00a0\"Number<\/li>\n
    27. \"\begin{array}{rrrrr}\"\text{Interval notation: } [2, \infty)\"\u00a0\"\"<\/li>\n
    28. \"\begin{array}{rrrrr}\"\text{Interval notation: } (-\infty, 5]\"\u00a0\"\"<\/li>\n
    29. \"\begin{array}{rrrrrrl}\"\text{Interval notation: } (8, \infty)\"\u00a0\"\"<\/li>\n
    30. \"\begin{array}{rrlrr}\"\text{Interval notation: } (-\infty, -3]\"\u00a0\"Number<\/li>\n
    31. \"\begin{array}{rrrrrrr}\"\text{Interval notation: } (1, \infty)\"\u00a0\"Number<\/li>\n
    32. \"\begin{array}{rrrrrrr}\"\text{Interval notation: } [0, \infty)\"\u00a0\"Number<\/li>\n
    33. \"\begin{array}{rrrrrrr}\"\text{Interval notation: } (-\infty, 0)\"\u00a0\"Number<\/li>\n
    34. \"\begin{array}{rrrrrrrrr}\"\text{Interval notation: } (2, \infty)\"\u00a0\"Number<\/li>\n
    35. \"\begin{array}{rrrrrrrrl}\"\text{False. No solution.}\"\u00a0\"Number<\/li>\n
    36. \"\begin{array}{rrrrrrrrrrrrr}\"\text{Interval notation: } (1, \infty)\"
      \n\"\"<\/li>\n
    37. \"\begin{array}{rrrrrrr}\"\text{Always true. Solution is all real numbers:} (-\infty, \infty)\"\u00a0\"Number<\/li>\n
    38. \"\begin{array}{rrrrrrrrl}\"\text{Interval notation: } (-\infty, 3]\"\u00a0\"Number<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":25,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1357","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1357","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":26,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1357\/revisions"}],"predecessor-version":[{"id":3803,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1357\/revisions\/3803"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1357\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1357"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1357"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1357"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}