{"id":1618,"date":"2019-07-29T17:57:13","date_gmt":"2019-07-29T21:57:13","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1618"},"modified":"2019-07-29T19:14:19","modified_gmt":"2019-07-29T23:14:19","slug":"answer-key-8-1","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-8-1\/","title":{"raw":"Answer Key 8.1","rendered":"Answer Key 8.1"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\dfrac{4(4)+2}{6}\\Rightarrow \\dfrac{16+2}{6}\\Rightarrow \\dfrac{18}{6}\\Rightarrow 3\\)<\/li>\r\n \t
  2. \\(\\dfrac{-2-3}{3(-2)-9}\\Rightarrow \\dfrac{-5}{-6-9}\\Rightarrow \\dfrac{-5}{-15}\\Rightarrow \\dfrac{1}{3}\\)<\/li>\r\n \t
  3. \\(\\dfrac{-4-3}{(-4)^2-4(-4)+3}\\Rightarrow \\dfrac{-7}{16+16+3}\\Rightarrow -\\dfrac{7}{35}\\Rightarrow -\\dfrac{1}{5}\\)<\/li>\r\n \t
  4. \\(\\dfrac{-1+2}{(-1)^2+3(-1)+2}\\Rightarrow \\dfrac{1}{1-3+2}\\Rightarrow \\dfrac{1}{0}\\Rightarrow \\text{Undefined}\\)<\/li>\r\n \t
  5. \\(\\dfrac{\\cancel{b}+2}{\\cancel{b^2+4b}+4}\\Rightarrow \\dfrac{2}{4}\\Rightarrow \\dfrac{1}{2}\\)<\/li>\r\n \t
  6. \\(\\dfrac{(4)^2-4-6}{4-3}\\Rightarrow \\dfrac{16-10}{1}\\Rightarrow \\dfrac{6}{1} \\Rightarrow 6\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\\r\nk&+&10&\\neq &0 \\\\\r\n&-&10&&-10 \\\\\r\n\\midrule\r\n&&k&\\neq &-10\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&18p(p&-&2) \\\\ \\\\\r\n&&18p&\\neq &0 \\\\\r\n&&p&\\neq &0 \\\\ \\\\\r\np&-&2&\\neq &0 \\\\\r\n&+&2&&+2 \\\\\r\n\\midrule\r\n&&p&\\neq &2\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrr}\r\n\\\\\r\n10m&\\neq& 0 \\\\\r\nm& \\neq &0\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(2(3x+10)\\Rightarrow \\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&+&10&\\neq &0 \\\\\r\n&-&10&&-10 \\\\\r\n\\midrule\r\n&&3x&\\neq &-10 \\\\ \\\\\r\n&&x&\\neq &-\\dfrac{10}{3}\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrr}\r\n\\\\\r\n5(r&+&2) \\\\\r\nr& \\neq & -2\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n3n(2n&+&1) \\\\\r\nn&\\neq &0 \\\\ \\\\\r\nn&\\neq &-\\dfrac{1}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrr}\r\n\\\\ \\\\\r\n(b-4)(b+8)&& \\\\\r\nb&\\neq &4 \\\\\r\nb&\\neq &-8\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrr}\r\n\\\\ \\\\ \\\\\r\n5v(7v&-&1) \\\\\r\nv&\\neq &0 \\\\\r\nv&\\neq &\\dfrac{1}{7}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\dfrac{21x^2}{18x}\\Rightarrow \\dfrac{\\cancel{3}\\cdot 7\\cdot \\cancel{x}\\cdot x}{\\cancel{3}\\cdot 6\\cdot \\cancel{x}}\\Rightarrow \\dfrac{7x}{6}\\)<\/li>\r\n \t
  16. \\(\\dfrac{12n}{4n^2}\\Rightarrow \\dfrac{3\\cdot \\cancel{4}\\cdot \\cancel{n}}{\\cancel{4}\\cdot \\cancel{n}\\cdot n}\\Rightarrow \\dfrac{3}{n}\\)<\/li>\r\n \t
  17. \\(\\dfrac{24a}{40a^2}\\Rightarrow \\dfrac{3\\cdot \\cancel{8}\\cdot \\cancel{a}}{5\\cdot \\cancel{8}\\cdot \\cancel{a}\\cdot a}\\Rightarrow \\dfrac{3}{5a}\\)<\/li>\r\n \t
  18. \\(\\dfrac{21k}{24k^2}\\Rightarrow \\dfrac{\\cancel{3}\\cdot 7\\cdot \\cancel{k}}{\\cancel{3}\\cdot 8\\cdot k}\\Rightarrow \\dfrac{7}{8k}\\)<\/li>\r\n \t
  19. \\(\\dfrac{18m-24}{60}\\Rightarrow \\dfrac{\\cancel{6}(3m-4)}{\\cancel{6}(10)}\\Rightarrow \\dfrac{3m-4}{10}\\)<\/li>\r\n \t
  20. \\(\\dfrac{n-9}{9n-81}\\Rightarrow \\dfrac{\\cancel{n-9}}{9\\cancel{(n-9)}}\\Rightarrow \\dfrac{1}{9}\\)<\/li>\r\n \t
  21. \\(\\dfrac{x+1}{x^2+8x+7}\\Rightarrow \\dfrac{\\cancel{x+1}}{\\cancel{(x+1)}(x+7)}\\Rightarrow \\dfrac{1}{x+7}\\)<\/li>\r\n \t
  22. \\(\\dfrac{28m+12}{36}\\Rightarrow \\dfrac{\\cancel{4}(7m+3)}{\\cancel{4}(9)}\\Rightarrow \\dfrac{7m+3}{9}\\)<\/li>\r\n \t
  23. \\(\\dfrac{n^2+4n-12}{n^2-7n+10}\\Rightarrow \\dfrac{(n+6)\\cancel{(n-2)}}{(n-5)\\cancel{(n-2)}}\\Rightarrow \\dfrac{n+6}{n-5}\\)<\/li>\r\n \t
  24. \\(\\dfrac{b^2+14b+48}{b^2+15b+56}\\Rightarrow \\dfrac{\\cancel{(b+8)}(b+6)}{\\cancel{(b+8)}(b+7)}\\Rightarrow \\dfrac{b+6}{b+7}\\)<\/li>\r\n \t
  25. \\(\\dfrac{9v+54}{v^2-4v-60}\\Rightarrow \\dfrac{9\\cancel{(v-6)}}{(v-10)\\cancel{(v+6)}}\\Rightarrow \\dfrac{9}{v-10}\\)<\/li>\r\n \t
  26. \\(\\dfrac{k^2-12k+32}{k^2-64}\\Rightarrow \\dfrac{\\cancel{(k-8)}(k-4)}{\\cancel{(k-8)}(k+8)}\\Rightarrow \\dfrac{k-4}{k+8}\\)<\/li>\r\n \t
  27. \\(\\dfrac{2n^2+19n-10}{9n+90}\\Rightarrow \\dfrac{(2n-1)\\cancel{(n+10)}}{9\\cancel{(n+10)}}\\Rightarrow \\dfrac{2n-1}{9}\\)<\/li>\r\n \t
  28. \\(\\dfrac{3x^2-29x+40}{5x^2-30x-80}\\Rightarrow \\dfrac{(3x-5)\\cancel{(x-8)}}{5(x+2)\\cancel{(x-8)}}\\Rightarrow \\dfrac{3x-5}{5(x+2)}\\)<\/li>\r\n \t
  29. \\(\\dfrac{2x^2-10x+8}{3x^2-7x+4}\\Rightarrow \\dfrac{2(x-4)\\cancel{(x-1)}}{(3x-4)\\cancel{(x-1)}}\\Rightarrow \\dfrac{2(x-4)}{3x-4}\\)<\/li>\r\n \t
  30. \\(\\dfrac{7n^2-32n+16}{4n-16}\\Rightarrow \\dfrac{(7n-4)\\cancel{(n-4)}}{4\\cancel{(n-4)}}\\Rightarrow \\dfrac{7n-4}{4}\\)<\/li>\r\n \t
  31. \\(\\dfrac{7a^2-26a-45}{6a^2-34a+20}\\Rightarrow \\dfrac{\\cancel{(a-5)}(7a+9)}{2(3a-2)\\cancel{(a-5)}}\\Rightarrow \\dfrac{7a+9}{2(3a-2)}\\)<\/li>\r\n \t
  32. \\(\\dfrac{4k^3-2k^2-2k}{k^3-18k^2+9k}\\Rightarrow \\dfrac{2k(2k^2-k-1)}{\\cancel{k}(k^2-18k+9)}\\Rightarrow \\dfrac{2(2k^2-k-1)}{k^2-18k+9}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\dfrac{4(4)+2}{6}\Rightarrow \dfrac{16+2}{6}\Rightarrow \dfrac{18}{6}\Rightarrow 3\"<\/li>\n
    2. \"\dfrac{-2-3}{3(-2)-9}\Rightarrow \dfrac{-5}{-6-9}\Rightarrow \dfrac{-5}{-15}\Rightarrow \dfrac{1}{3}\"<\/li>\n
    3. \"\dfrac{-4-3}{(-4)^2-4(-4)+3}\Rightarrow \dfrac{-7}{16+16+3}\Rightarrow -\dfrac{7}{35}\Rightarrow -\dfrac{1}{5}\"<\/li>\n
    4. \"\dfrac{-1+2}{(-1)^2+3(-1)+2}\Rightarrow \dfrac{1}{1-3+2}\Rightarrow \dfrac{1}{0}\Rightarrow \text{Undefined}\"<\/li>\n
    5. \"\dfrac{\cancel{b}+2}{\cancel{b^2+4b}+4}\Rightarrow \dfrac{2}{4}\Rightarrow \dfrac{1}{2}\"<\/li>\n
    6. \"\dfrac{(4)^2-4-6}{4-3}\Rightarrow \dfrac{16-10}{1}\Rightarrow \dfrac{6}{1} \Rightarrow 6\"<\/li>\n
    7. \"\begin{array}{rrrrr}<\/li>\n
    8. \"\begin{array}{rrrrr}<\/li>\n
    9. \"\begin{array}{rrr}<\/li>\n
    10. \"2(3x+10)\Rightarrow \begin{array}{rrrrr}<\/li>\n
    11. \"\begin{array}{rrr}<\/li>\n
    12. \"\begin{array}{rrr}<\/li>\n
    13. \"\begin{array}{rrr}<\/li>\n
    14. \"\begin{array}{rrr}<\/li>\n
    15. \"\dfrac{21x^2}{18x}\Rightarrow \dfrac{\cancel{3}\cdot 7\cdot \cancel{x}\cdot x}{\cancel{3}\cdot 6\cdot \cancel{x}}\Rightarrow \dfrac{7x}{6}\"<\/li>\n
    16. \"\dfrac{12n}{4n^2}\Rightarrow \dfrac{3\cdot \cancel{4}\cdot \cancel{n}}{\cancel{4}\cdot \cancel{n}\cdot n}\Rightarrow \dfrac{3}{n}\"<\/li>\n
    17. \"\dfrac{24a}{40a^2}\Rightarrow \dfrac{3\cdot \cancel{8}\cdot \cancel{a}}{5\cdot \cancel{8}\cdot \cancel{a}\cdot a}\Rightarrow \dfrac{3}{5a}\"<\/li>\n
    18. \"\dfrac{21k}{24k^2}\Rightarrow \dfrac{\cancel{3}\cdot 7\cdot \cancel{k}}{\cancel{3}\cdot 8\cdot k}\Rightarrow \dfrac{7}{8k}\"<\/li>\n
    19. \"\dfrac{18m-24}{60}\Rightarrow \dfrac{\cancel{6}(3m-4)}{\cancel{6}(10)}\Rightarrow \dfrac{3m-4}{10}\"<\/li>\n
    20. \"\dfrac{n-9}{9n-81}\Rightarrow \dfrac{\cancel{n-9}}{9\cancel{(n-9)}}\Rightarrow \dfrac{1}{9}\"<\/li>\n
    21. \"\dfrac{x+1}{x^2+8x+7}\Rightarrow \dfrac{\cancel{x+1}}{\cancel{(x+1)}(x+7)}\Rightarrow \dfrac{1}{x+7}\"<\/li>\n
    22. \"\dfrac{28m+12}{36}\Rightarrow \dfrac{\cancel{4}(7m+3)}{\cancel{4}(9)}\Rightarrow \dfrac{7m+3}{9}\"<\/li>\n
    23. \"\dfrac{n^2+4n-12}{n^2-7n+10}\Rightarrow \dfrac{(n+6)\cancel{(n-2)}}{(n-5)\cancel{(n-2)}}\Rightarrow \dfrac{n+6}{n-5}\"<\/li>\n
    24. \"\dfrac{b^2+14b+48}{b^2+15b+56}\Rightarrow \dfrac{\cancel{(b+8)}(b+6)}{\cancel{(b+8)}(b+7)}\Rightarrow \dfrac{b+6}{b+7}\"<\/li>\n
    25. \"\dfrac{9v+54}{v^2-4v-60}\Rightarrow \dfrac{9\cancel{(v-6)}}{(v-10)\cancel{(v+6)}}\Rightarrow \dfrac{9}{v-10}\"<\/li>\n
    26. \"\dfrac{k^2-12k+32}{k^2-64}\Rightarrow \dfrac{\cancel{(k-8)}(k-4)}{\cancel{(k-8)}(k+8)}\Rightarrow \dfrac{k-4}{k+8}\"<\/li>\n
    27. \"\dfrac{2n^2+19n-10}{9n+90}\Rightarrow \dfrac{(2n-1)\cancel{(n+10)}}{9\cancel{(n+10)}}\Rightarrow \dfrac{2n-1}{9}\"<\/li>\n
    28. \"\dfrac{3x^2-29x+40}{5x^2-30x-80}\Rightarrow \dfrac{(3x-5)\cancel{(x-8)}}{5(x+2)\cancel{(x-8)}}\Rightarrow \dfrac{3x-5}{5(x+2)}\"<\/li>\n
    29. \"\dfrac{2x^2-10x+8}{3x^2-7x+4}\Rightarrow \dfrac{2(x-4)\cancel{(x-1)}}{(3x-4)\cancel{(x-1)}}\Rightarrow \dfrac{2(x-4)}{3x-4}\"<\/li>\n
    30. \"\dfrac{7n^2-32n+16}{4n-16}\Rightarrow \dfrac{(7n-4)\cancel{(n-4)}}{4\cancel{(n-4)}}\Rightarrow \dfrac{7n-4}{4}\"<\/li>\n
    31. \"\dfrac{7a^2-26a-45}{6a^2-34a+20}\Rightarrow \dfrac{\cancel{(a-5)}(7a+9)}{2(3a-2)\cancel{(a-5)}}\Rightarrow \dfrac{7a+9}{2(3a-2)}\"<\/li>\n
    32. \"\dfrac{4k^3-2k^2-2k}{k^3-18k^2+9k}\Rightarrow \dfrac{2k(2k^2-k-1)}{\cancel{k}(k^2-18k+9)}\Rightarrow \dfrac{2(2k^2-k-1)}{k^2-18k+9}\"<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":69,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1618","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1618","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":4,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1618\/revisions"}],"predecessor-version":[{"id":1622,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1618\/revisions\/1622"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1618\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1618"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1618"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1618"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}