{"id":1694,"date":"2021-12-02T19:39:03","date_gmt":"2021-12-03T00:39:03","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-4-1\/"},"modified":"2022-11-02T10:37:15","modified_gmt":"2022-11-02T14:37:15","slug":"answer-key-4-1","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-4-1\/","title":{"raw":"Answer Key 4.1","rendered":"Answer Key 4.1"},"content":{"raw":"
    \n \t
  1. [latex](-5, \\infty)[\/latex]\u00a0 \u00a0 \u00a0\"-5,<\/li>\n \t
  2. [latex](4, \\infty)[\/latex]\u00a0 \u00a0 \u00a0 \u00a0\"4,<\/li>\n \t
  3. [latex](-2, \\infty)[\/latex]\u00a0 \u00a0\"-2,<\/li>\n \t
  4. [latex](-\\infty, 1][\/latex]\u00a0 \u00a0 \u00a0\"-<\/li>\n \t
  5. [latex](-\\infty, 5][\/latex]\u00a0 \u00a0\u00a0\"-<\/li>\n \t
  6. [latex](-5, \\infty)[\/latex]\u00a0 \u00a0 \u00a0\"-5,<\/li>\n \t
  7. [latex]x>-5\\hspace{0.25in} (-5, \\infty)[\/latex]\u00a0 \u00a0 \u00a0\"x -5, -5, inifinity\" width=\"367\" height=\"71\"><\/li>\n \t
  8. [latex]x>0\\hspace{0.25in} (0, \\infty)[\/latex]\u00a0 \u00a0 \u00a0 \u00a0\u00a0\"(x 0), 0, inifinity \" width=\"382\" height=\"65\"><\/li>\n \t
  9. [latex]x\\ge -3 \\hspace{0.25in} [-3, \\infty)[\/latex]\u00a0 \u00a0 \u00a0\"x or equal to -3, (-3, inifinity)\" width=\"388\" height=\"57\"><\/li>\n \t
  10. [latex]x\\le 6 \\hspace{0.25in} (-\\infty, 6][\/latex]\u00a0 \u00a0 \u00a0\"x<\/li>\n \t
  11. [latex]x\\le -1 \\hspace{0.25in} (-\\infty, -1][\/latex]\u00a0 \u00a0 \u00a0\"x<\/li>\n \t
  12. [latex]x < 6 \\hspace{0.25in} (-\\infty, 6)[\/latex]\u00a0 \u00a0 \u00a0\u00a0\"x<\/li>\n \t
  13. [latex](\\dfrac{x}{11}\\ge 10)(11)[\/latex]\n[latex]x\\ge110[\/latex]\n[latex]\\text{Interval notation: }[110, \u221e)[\/latex]\"Number<\/li>\n \t
  14. [latex](-2 \\le \\dfrac{n}{13})(13)[\/latex]\n[latex]-26\\le n[\/latex]\n[latex]\\text{Interval notation: } [-26, \u221e)[\/latex]\"Number<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrlr}\n2&+&r&<&3 \\\\\n-2&&&& -2 \\\\\n\\hline\n&&r&<&1\\\\\n\\end{array}[\/latex]\n[latex]\\text{Interval notation: }(-\u221e, 1)[\/latex]\"Number<\/li>\n \t
  16. [latex](\\dfrac{m}{5}\\le-\\dfrac{6}{5})(5)[\/latex]\n[latex]m \\le -6[\/latex]\n[latex]\\text{Interval notation: } (-\\infty, -6][\/latex]\"Number<\/li>\n \t
  17. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n8&+&\\dfrac{n}{3}&\\ge & 6 & \\\\\n-8&&&&-8 & \\\\\n\\hline\n&&(\\dfrac{n}{3} &\\ge & -2)& (3) \\\\ \\\\\n&&n & \\ge & -6 &\\\\\n\\end{array}\\\\ \\text{Interval notation: } [-6, \\infty)[\/latex] \"Number<\/li>\n \t
  18. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n11&>&8&+ & \\dfrac{x}{2} \\\\\n-8&&-8&& \\\\\n\\hline\n(3 &> & \\dfrac{x}{2})& (2)& \\\\ \\\\\n6 & > & x &&\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, 6)[\/latex] \"Number<\/li>\n \t
  19. [latex]\\left(2>\\dfrac{(a-2)}{5}\\right)(5)[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n10&>&a&-&2 \\\\\n+2&&&+&2 \\\\\n\\hline\n12&>&a&&\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, 12)[\/latex] \"Number<\/li>\n \t
  20. [latex]\\left(\\dfrac{(v-9)}{-4}\\le 2 \\right)(-4)[\/latex]\n[latex]\\begin{array}{rrrrr}\nv&-&9&\\ge &-8 \\\\\n&+&9&&+9 \\\\\n\\hline\n&&v&\\ge &1\n\\end{array}\\\\ \\text{Interval notation: } [1, \\infty)[\/latex]\u00a0 \"Number<\/li>\n \t
  21. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrl}\n-47&\\ge &8&-& 5x \\\\\n-8&&-8&& \\\\\n\\hline\n\\dfrac{-55}{-5}&\\ge &\\dfrac{-5x}{-5} && \\\\ \\\\\n11& \\le & x &&\n\\end{array}\\\\ \\text{Interval notation: } [11, \\infty)[\/latex]\u00a0 \"Number<\/li>\n \t
  22. [latex]\\left(\\dfrac{(6+x)}{12}\\le -1 \\right)(12)[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n6&+&x&\\le &-12 \\\\\n-6&&&&-6 \\\\\n\\hline\n&&x&\\le &-18\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, -18][\/latex] \"Number<\/li>\n \t
  23. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrl}\n\\dfrac{-2}{-2}(3&+ &k)&<& \\dfrac{-44}{-2} \\\\ \\\\\n3&+ &k &>&22 \\\\\n-3&&&&-3 \\\\\n\\hline\n&& k&>&19\\\\\n\\end{array}\\\\ \\text{Interval notation: } (19, \\infty)[\/latex] \"Number<\/li>\n \t
  24. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n-7n&- &10&\\ge &60 \\\\\n&+&10&&+10 \\\\\n\\hline\n&&\\dfrac{-7n}{-7}&\\ge & \\dfrac{70}{-7} \\\\ \\\\\n&&n&\\le &-10\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, -10][\/latex] \"Number<\/li>\n \t
  25. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrl}\n\\dfrac{18}{-2}&<&\\dfrac{-2}{-2}(-8&+&p) \\\\ \\\\\n-9&>&-8&+&p \\\\\n+8&&+8&& \\\\\n\\hline\n-1&>&p&&\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, -1)[\/latex]\u00a0 \"Number<\/li>\n \t
  26. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n(5&>& \\dfrac{x}{5}&+&1)(5)\\\\\n25&\\ge &x&+ &5 \\\\\n-5&&&&-5 \\\\\n\\hline\n20&\\ge &x& &\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, 20][\/latex]\u00a0 \"Number<\/li>\n \t
  27. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n\\dfrac{24}{-6}&\\ge &\\dfrac{-6}{-6}(m&-&6) \\\\ \\\\\n-4&\\le &m&-&6 \\\\\n+6&&&+&6 \\\\\n\\hline\n2&\\le &m&&\\\\\n\\end{array}\\\\ \\text{Interval notation: } [2, \\infty)[\/latex] \"\"<\/li>\n \t
  28. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n\\dfrac{-8}{-8}(n&-&5)&\\ge &\\dfrac{0}{-8} \\\\ \\\\\nn&-&5&\\le &0 \\\\\n&+&5&&+5 \\\\\n\\hline\n&&n&\\le &5\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, 5][\/latex] \"\"<\/li>\n \t
  29. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n-r&-&5(r&-&6)&<&-18 \\\\\n-r&-&5r&+&30&<&-18 \\\\\n&&&-&30&&-30 \\\\\n\\hline\n&&&&\\dfrac{-6r}{-6}&<&\\dfrac{-48}{-6} \\\\ \\\\\n&&&&r&>&8 \\\\\n\\end{array}\\\\ \\text{Interval notation: } (8, \\infty)[\/latex] \"\"<\/li>\n \t
  30. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrlrr}\n\\dfrac{-60}{-4}&\\ge &\\dfrac{-4}{-4}(-6x&-&3) \\\\ \\\\\n15&\\le &-6x&-&3 \\\\\n+3&&&+&3 \\\\\n\\hline\n\\dfrac{18}{-6}&\\le&\\dfrac{-6x}{-6}&& \\\\ \\\\\n-3&\\ge &x &&\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, -3][\/latex] \"Number<\/li>\n \t
  31. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&&\\dfrac{24+4b}{4}&<&\\dfrac{4}{4}(1&+&6b) \\\\ \\\\\n6&+&b&<&1&+&6b \\\\\n-1&-&b&&-1&-&b \\\\\n\\hline\n&&\\dfrac{5}{5}&<&\\dfrac{5b}{5}&& \\\\ \\\\\n&&b&>&1&&\\\\\n\\end{array}\\\\ \\text{Interval notation: } (1, \\infty)[\/latex] \"Number<\/li>\n \t
  32. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n-8(2&-&2n)&\\ge &-16&+&n \\\\\n-16&+&16n& \\ge & -16 & + & n\\\\\n+16&-&n&&+16 &-& n\\\\\n\\hline\n&&15n& \\ge &0 &&\\\\\n&&n& \\ge &0 &&\\\\\n\\end{array}\\\\ \\text{Interval notation: } [0, \\infty)[\/latex] \"Number<\/li>\n \t
  33. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&&\\dfrac{-5v-5}{-5}&<&\\dfrac{-5}{-5}(4v&+&1) \\\\ \\\\\nv&+&1&>&4v&+&1 \\\\\n-v&-&1&&-v&-&1 \\\\\n\\hline\n&&\\dfrac{0}{3}&>&\\dfrac{3v}{3}&& \\\\ \\\\\n&&v&<&0&&\\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, 0)[\/latex] \"Number<\/li>\n \t
  34. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n-36&+&6x&>&-8(x&+&2)&+&4x \\\\\n-36&+&6x&>&-8x&-&16&+&4x \\\\\n+16&-&6x&&-6x&+&16&& \\\\\n\\hline\n&&\\dfrac{-20}{-10}&>&\\dfrac{-10x}{-10}&&&& \\\\ \\\\\n&&x&>&2&&&& \\\\\n\\end{array}\\\\ \\text{Interval notation: } (2, \\infty)[\/latex] \"Number<\/li>\n \t
  35. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrl}\n4&+&2(a&+&5)&<&-2(-a&-&4) \\\\\n4&+&2a&+&10&<&2a&+&8 \\\\\n-4&-&2a&-&10&&-2a&-&10-4 \\\\\n\\hline\n&&0&<&-6&&&&\n\\end{array}\\\\ \\text{False. No solution.}[\/latex] \"Number<\/li>\n \t
  36. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrrrr}\n3(n&+&3)&+&7(8&-&8n)&<&5n&+&5&+&2 \\\\\n3n&+&9&+&56&-&56n&<&5n&+&7&& \\\\\n&&&&-53n&+&65&<&5n&+&7&& \\\\\n&&&&-5n&-&65&&-5n&-&65&& \\\\\n\\hline\n&&&&&&-58n&<&-58&&&& \\\\\n&&&&&&n&>&1&&&& \\\\\n\\end{array}\\\\ \\text{Interval notation: } (1, \\infty)[\/latex]\n\"\"<\/li>\n \t
  37. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n-(k&-&2)&>&-k&-&20 \\\\\n-k&+&2&>&-k&-&20 \\\\\n+k&-&2&&+k&-&2 \\\\\n\\hline\n&&0&>&-22&& \\\\\n\\end{array}\\\\ \\text{Always true. Solution is all real numbers:} (-\\infty, \\infty)[\/latex] \"Number<\/li>\n \t
  38. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrl}\n-(4&-&5p)&+&3&\\ge &-2(8&-&5p) \\\\\n-4&+&5p&+&3&\\ge &-16&+&10p \\\\\n&&-1&+&5p&\\ge &-16&+&10p \\\\\n&&+1&-&10p&&+1&-&10p \\\\\n\\hline\n&&&&\\dfrac{-5p}{-5}&\\ge &\\dfrac{-15}{-5}&& \\\\ \\\\\n&&&&p&\\le &3&& \\\\\n\\end{array}\\\\ \\text{Interval notation: } (-\\infty, 3][\/latex] \"Number<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex](-5, \\infty)[\/latex]\u00a0 \u00a0 \u00a0\"-5,<\/li>\n
    2. [latex](4, \\infty)[\/latex]\u00a0 \u00a0 \u00a0 \u00a0\"4,<\/li>\n
    3. [latex](-2, \\infty)[\/latex]\u00a0 \u00a0\"-2,<\/li>\n
    4. [latex](-\\infty, 1][\/latex]\u00a0 \u00a0 \u00a0\"-<\/li>\n
    5. [latex](-\\infty, 5][\/latex]\u00a0 \u00a0\u00a0\"-<\/li>\n
    6. [latex](-5, \\infty)[\/latex]\u00a0 \u00a0 \u00a0\"-5,<\/li>\n
    7. [latex]x>-5\\hspace{0.25in} (-5, \\infty)[\/latex]\u00a0 \u00a0 \u00a0\"image\" -5, -5, inifinity” width=”367″ height=”71″><\/li>\n
    8. [latex]x>0\\hspace{0.25in} (0, \\infty)[\/latex]\u00a0 \u00a0 \u00a0 \u00a0\u00a0\"image\" 0), 0, inifinity ” width=”382″ height=”65″><\/li>\n
    9. [latex]x\\ge -3 \\hspace{0.25in} [-3, \\infty)[\/latex]\u00a0 \u00a0 \u00a0\"image\" or equal to -3, (-3, inifinity)” width=”388″ height=”57″><\/li>\n
    10. [latex]x\\le 6 \\hspace{0.25in} (-\\infty, 6][\/latex]\u00a0 \u00a0 \u00a0\"x<\/li>\n
    11. [latex]x\\le -1 \\hspace{0.25in} (-\\infty, -1][\/latex]\u00a0 \u00a0 \u00a0\"x<\/li>\n
    12. [latex]x < 6 \\hspace{0.25in} (-\\infty, 6)[\/latex]\u00a0 \u00a0 \u00a0\u00a0\"x<\/li>\n
    13. [latex](\\dfrac{x}{11}\\ge 10)(11)[\/latex]
      \n[latex]x\\ge110[\/latex]
      \n[latex]\\text{Interval notation: }[110, \u221e)[\/latex]\"Number<\/li>\n
    14. [latex](-2 \\le \\dfrac{n}{13})(13)[\/latex]
      \n[latex]-26\\le n[\/latex]
      \n[latex]\\text{Interval notation: } [-26, \u221e)[\/latex]\"Number<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrlr} 2&+&r&<&3 \\\\ -2&&&& -2 \\\\ \\hline &&r&<&1\\\\ \\end{array}[\/latex]\n[latex]\\text{Interval notation: }(-\u221e, 1)[\/latex]\"Number<\/li>\n
    16. [latex](\\dfrac{m}{5}\\le-\\dfrac{6}{5})(5)[\/latex]
      \n[latex]m \\le -6[\/latex]
      \n[latex]\\text{Interval notation: } (-\\infty, -6][\/latex]\"Number<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} 8&+&\\dfrac{n}{3}&\\ge & 6 & \\\\ -8&&&&-8 & \\\\ \\hline &&(\\dfrac{n}{3} &\\ge & -2)& (3) \\\\ \\\\ &&n & \\ge & -6 &\\\\ \\end{array}\\\\ \\text{Interval notation: } [-6, \\infty)[\/latex] \"Number<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 11&>&8&+ & \\dfrac{x}{2} \\\\ -8&&-8&& \\\\ \\hline (3 &> & \\dfrac{x}{2})& (2)& \\\\ \\\\ 6 & > & x &&\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, 6)[\/latex] \"Number<\/li>\n
    19. [latex]\\left(2>\\dfrac{(a-2)}{5}\\right)(5)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 10&>&a&-&2 \\\\ +2&&&+&2 \\\\ \\hline 12&>&a&&\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, 12)[\/latex] \"Number<\/li>\n
    20. [latex]\\left(\\dfrac{(v-9)}{-4}\\le 2 \\right)(-4)[\/latex]
      \n[latex]\\begin{array}{rrrrr} v&-&9&\\ge &-8 \\\\ &+&9&&+9 \\\\ \\hline &&v&\\ge &1 \\end{array}\\\\ \\text{Interval notation: } [1, \\infty)[\/latex]\u00a0 \"Number<\/li>\n
    21. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} -47&\\ge &8&-& 5x \\\\ -8&&-8&& \\\\ \\hline \\dfrac{-55}{-5}&\\ge &\\dfrac{-5x}{-5} && \\\\ \\\\ 11& \\le & x && \\end{array}\\\\ \\text{Interval notation: } [11, \\infty)[\/latex]\u00a0 \"Number<\/li>\n
    22. [latex]\\left(\\dfrac{(6+x)}{12}\\le -1 \\right)(12)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 6&+&x&\\le &-12 \\\\ -6&&&&-6 \\\\ \\hline &&x&\\le &-18\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, -18][\/latex] \"Number<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} \\dfrac{-2}{-2}(3&+ &k)&<& \\dfrac{-44}{-2} \\\\ \\\\ 3&+ &k &>&22 \\\\ -3&&&&-3 \\\\ \\hline && k&>&19\\\\ \\end{array}\\\\ \\text{Interval notation: } (19, \\infty)[\/latex] \"Number<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -7n&- &10&\\ge &60 \\\\ &+&10&&+10 \\\\ \\hline &&\\dfrac{-7n}{-7}&\\ge & \\dfrac{70}{-7} \\\\ \\\\ &&n&\\le &-10\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, -10][\/latex] \"Number<\/li>\n
    25. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} \\dfrac{18}{-2}&<&\\dfrac{-2}{-2}(-8&+&p) \\\\ \\\\ -9&>&-8&+&p \\\\ +8&&+8&& \\\\ \\hline -1&>&p&&\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, -1)[\/latex]\u00a0 \"Number<\/li>\n
    26. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} (5&>& \\dfrac{x}{5}&+&1)(5)\\\\ 25&\\ge &x&+ &5 \\\\ -5&&&&-5 \\\\ \\hline 20&\\ge &x& &\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, 20][\/latex]\u00a0 \"Number<\/li>\n
    27. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} \\dfrac{24}{-6}&\\ge &\\dfrac{-6}{-6}(m&-&6) \\\\ \\\\ -4&\\le &m&-&6 \\\\ +6&&&+&6 \\\\ \\hline 2&\\le &m&&\\\\ \\end{array}\\\\ \\text{Interval notation: } [2, \\infty)[\/latex] \"\"<\/li>\n
    28. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} \\dfrac{-8}{-8}(n&-&5)&\\ge &\\dfrac{0}{-8} \\\\ \\\\ n&-&5&\\le &0 \\\\ &+&5&&+5 \\\\ \\hline &&n&\\le &5\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, 5][\/latex] \"\"<\/li>\n
    29. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} -r&-&5(r&-&6)&<&-18 \\\\ -r&-&5r&+&30&<&-18 \\\\ &&&-&30&&-30 \\\\ \\hline &&&&\\dfrac{-6r}{-6}&<&\\dfrac{-48}{-6} \\\\ \\\\ &&&&r&>&8 \\\\ \\end{array}\\\\ \\text{Interval notation: } (8, \\infty)[\/latex] \"\"<\/li>\n
    30. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlrr} \\dfrac{-60}{-4}&\\ge &\\dfrac{-4}{-4}(-6x&-&3) \\\\ \\\\ 15&\\le &-6x&-&3 \\\\ +3&&&+&3 \\\\ \\hline \\dfrac{18}{-6}&\\le&\\dfrac{-6x}{-6}&& \\\\ \\\\ -3&\\ge &x &&\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, -3][\/latex] \"Number<\/li>\n
    31. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &&\\dfrac{24+4b}{4}&<&\\dfrac{4}{4}(1&+&6b) \\\\ \\\\ 6&+&b&<&1&+&6b \\\\ -1&-&b&&-1&-&b \\\\ \\hline &&\\dfrac{5}{5}&<&\\dfrac{5b}{5}&& \\\\ \\\\ &&b&>&1&&\\\\ \\end{array}\\\\ \\text{Interval notation: } (1, \\infty)[\/latex] \"Number<\/li>\n
    32. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} -8(2&-&2n)&\\ge &-16&+&n \\\\ -16&+&16n& \\ge & -16 & + & n\\\\ +16&-&n&&+16 &-& n\\\\ \\hline &&15n& \\ge &0 &&\\\\ &&n& \\ge &0 &&\\\\ \\end{array}\\\\ \\text{Interval notation: } [0, \\infty)[\/latex] \"Number<\/li>\n
    33. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &&\\dfrac{-5v-5}{-5}&<&\\dfrac{-5}{-5}(4v&+&1) \\\\ \\\\ v&+&1&>&4v&+&1 \\\\ -v&-&1&&-v&-&1 \\\\ \\hline &&\\dfrac{0}{3}&>&\\dfrac{3v}{3}&& \\\\ \\\\ &&v&<&0&&\\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, 0)[\/latex] \"Number<\/li>\n
    34. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} -36&+&6x&>&-8(x&+&2)&+&4x \\\\ -36&+&6x&>&-8x&-&16&+&4x \\\\ +16&-&6x&&-6x&+&16&& \\\\ \\hline &&\\dfrac{-20}{-10}&>&\\dfrac{-10x}{-10}&&&& \\\\ \\\\ &&x&>&2&&&& \\\\ \\end{array}\\\\ \\text{Interval notation: } (2, \\infty)[\/latex] \"Number<\/li>\n
    35. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrl} 4&+&2(a&+&5)&<&-2(-a&-&4) \\\\ 4&+&2a&+&10&<&2a&+&8 \\\\ -4&-&2a&-&10&&-2a&-&10-4 \\\\ \\hline &&0&<&-6&&&& \\end{array}\\\\ \\text{False. No solution.}[\/latex] \"Number<\/li>\n
    36. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrrrr} 3(n&+&3)&+&7(8&-&8n)&<&5n&+&5&+&2 \\\\ 3n&+&9&+&56&-&56n&<&5n&+&7&& \\\\ &&&&-53n&+&65&<&5n&+&7&& \\\\ &&&&-5n&-&65&&-5n&-&65&& \\\\ \\hline &&&&&&-58n&<&-58&&&& \\\\ &&&&&&n&>&1&&&& \\\\ \\end{array}\\\\ \\text{Interval notation: } (1, \\infty)[\/latex]
      \n\"\"<\/li>\n
    37. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} -(k&-&2)&>&-k&-&20 \\\\ -k&+&2&>&-k&-&20 \\\\ +k&-&2&&+k&-&2 \\\\ \\hline &&0&>&-22&& \\\\ \\end{array}\\\\ \\text{Always true. Solution is all real numbers:} (-\\infty, \\infty)[\/latex] \"Number<\/li>\n
    38. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrl} -(4&-&5p)&+&3&\\ge &-2(8&-&5p) \\\\ -4&+&5p&+&3&\\ge &-16&+&10p \\\\ &&-1&+&5p&\\ge &-16&+&10p \\\\ &&+1&-&10p&&+1&-&10p \\\\ \\hline &&&&\\dfrac{-5p}{-5}&\\ge &\\dfrac{-15}{-5}&& \\\\ \\\\ &&&&p&\\le &3&& \\\\ \\end{array}\\\\ \\text{Interval notation: } (-\\infty, 3][\/latex] \"Number<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":30,"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-1694","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\/1694","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\/1694\/revisions"}],"predecessor-version":[{"id":1695,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1694\/revisions\/1695"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1694\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1694"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1694"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1694"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}