{"id":1627,"date":"2019-07-30T12:04:01","date_gmt":"2019-07-30T16:04:01","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1627"},"modified":"2019-07-30T12:58:11","modified_gmt":"2019-07-30T16:58:11","slug":"answer-key-8-2","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-8-2\/","title":{"raw":"Answer Key 8.2","rendered":"Answer Key 8.2"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\dfrac{8x^2}{9}\\cdot \\dfrac{9}{2}\\Rightarrow \\dfrac{\\cancel{2}\\cdot 4\\cdot x^2}{\\cancel{9}}\\cdot \\dfrac{\\cancel{9}}{\\cancel{2}}\\Rightarrow 4x^2\\)<\/li>\r\n \t
  2. \\(\\dfrac{8x}{3}\\div \\dfrac{4x}{7}\\Rightarrow \\dfrac{8x}{3}\\cdot \\dfrac{7}{4x} \\Rightarrow \\dfrac{2\\cdot \\cancel{4}\\cdot \\cancel{x}}{3}\\cdot \\dfrac{7}{\\cancel{4}\\cdot \\cancel{x}}\\Rightarrow \\dfrac{14}{3}\\)<\/li>\r\n \t
  3. \\(\\dfrac{5x^2}{4}\\cdot \\dfrac{6}{5}\\Rightarrow \\dfrac{\\cancel{5}\\cdot x^2}{2\\cdot \\cancel{2}}\\cdot \\dfrac{\\cancel{2}\\cdot 3}{\\cancel{5}}\\Rightarrow \\dfrac{3x^2}{2}\\)<\/li>\r\n \t
  4. \\(\\dfrac{10p}{5}\\div \\dfrac{8}{10}\\Rightarrow \\dfrac{10p}{5}\\cdot \\dfrac{10}{8}\\Rightarrow \\dfrac{\\cancel{2}\\cdot 5\\cdot p}{\\cancel{5}}\\cdot \\dfrac{\\cancel{2} \\cdot \\cancel{5}}{2\\cdot \\cancel{2} \\cdot \\cancel{2}}\\Rightarrow \\dfrac{5p}{2}\\)<\/li>\r\n \t
  5. \\(\\dfrac{\\cancel{(m-6)}}{7\\cancel{(7m-5)}}\\cdot \\dfrac{5m\\cancel{(7m-5)}}{\\cancel{m-6}}\\Rightarrow \\dfrac{5m}{7}\\)<\/li>\r\n \t
  6. \\(\\dfrac{7(n-2)}{10(n+3)}\\div \\dfrac{n-2}{(n+3)}\\Rightarrow \\dfrac{7\\cancel{(n-2)}}{10\\cancel{(n+3)}}\\cdot \\dfrac{\\cancel{(n+3)}}{\\cancel{n-2}}\\Rightarrow \\dfrac{7}{10}\\)<\/li>\r\n \t
  7. \\(\\dfrac{7r}{7r(r+10)}\\div \\dfrac{r-6}{(r-6)^2}\\Rightarrow \\dfrac{7r}{7r(r+10)}\\cdot \\dfrac{(r-6)^2}{r-6}\\Rightarrow \\dfrac{\\cancel{7r}}{\\cancel{7r}(r+10)}\\cdot \\dfrac{(r-6)\\cancel{(r-6)}}{\\cancel{r-6}}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{r-6}{r+10}\\)<\/li>\r\n \t
  8. \\(\\dfrac{6x(x+4)}{(x-3)}\\cdot \\dfrac{(x-3)(x-6)}{6x(x-6)}\\Rightarrow \\dfrac{\\cancel{6x}(x+4)}{\\cancel{(x-3)}}\\cdot \\dfrac{\\cancel{(x-3)}\\cancel{(x-6)}}{\\cancel{6x}\\cancel{(x-6)}}\\Rightarrow x+4\\)<\/li>\r\n \t
  9. \\(\\dfrac{x-10}{35x+21}\\div \\dfrac{7}{35x+21}\\Rightarrow \\dfrac{x-10}{7\\cancel{(5x+3)}}\\cdot \\dfrac{\\cancel{7}\\cancel{(5x+3)}}{\\cancel{7}}\\Rightarrow \\dfrac{x-10}{7}\\)<\/li>\r\n \t
  10. \\(\\dfrac{v-1}{4}\\cdot \\dfrac{4}{v^2-11v+10}\\Rightarrow \\dfrac{\\cancel{v-1}}{\\cancel{4}}\\Rightarrow \\dfrac{\\cancel{4}}{\\cancel{(v-1)}(v-10)}\\Rightarrow \\dfrac{1}{v-10}\\)<\/li>\r\n \t
  11. \\(\\dfrac{x^2-6x-7}{x+5}\\cdot \\dfrac{x+5}{x-7}\\Rightarrow \\dfrac{\\cancel{(x-7)}(x+1)}{\\cancel{(x+5)}}\\cdot \\dfrac{\\cancel{(x+5)}}{\\cancel{(x-7)}}\\Rightarrow x+1\\)<\/li>\r\n \t
  12. \\(\\dfrac{1}{a-6}\\cdot \\dfrac{8a+80}{8}\\Rightarrow \\dfrac{1}{a-6}\\cdot \\dfrac{\\cancel{8}(a+10)}{\\cancel{8}}\\Rightarrow \\dfrac{a+10}{a-6}\\)<\/li>\r\n \t
  13. \\(\\dfrac{4m+36}{m+9}\\cdot \\dfrac{m-5}{5m^2}\\Rightarrow \\dfrac{4\\cancel{(m+9)}}{\\cancel{m+9}}\\cdot \\dfrac{m-5}{5m^2}\\Rightarrow \\dfrac{4(m-5)}{5m^2}\\)<\/li>\r\n \t
  14. \\(\\dfrac{2r}{r+6}\\div \\dfrac{2r}{74+42}\\Rightarrow \\dfrac{\\cancel{2r}}{\\cancel{r+6}}\\cdot \\dfrac{7\\cancel{(r+6)}}{\\cancel{2r}}\\Rightarrow 7\\)<\/li>\r\n \t
  15. \\(\\dfrac{n-7}{6n-12}\\cdot \\dfrac{12-6n}{n^2-13n+42}\\Rightarrow \\dfrac{\\cancel{(n-7)}}{\\cancel{6}(n-2)}\\cdot \\dfrac{\\cancel{6}(2-n)}{(n-6)\\cancel{(n-7)}}\\Rightarrow \\dfrac{-1\\cancel{(n-2)}}{\\cancel{(n-2)}(n-6)}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{-1}{n-6}\\)<\/li>\r\n \t
  16. \\(\\dfrac{x^2+11x+24}{6x^3+18x^2}\\cdot \\dfrac{6x^3+6x^2}{x^2+5x-24}\\Rightarrow \\dfrac{\\cancel{(x+3)}\\cancel{(x+8)}}{\\cancel{6x^2}\\cancel{(x+3)}}\\cdot \\dfrac{\\cancel{6x^2}(x+1)}{\\cancel{(x+8)}(x-3)}\\Rightarrow \\dfrac{x+1}{x-3}\\)<\/li>\r\n \t
  17. \\(\\dfrac{27a+36}{9a+63}\\div \\dfrac{6a+8}{2}\\Rightarrow \\dfrac{\\cancel{9}\\cancel{(3a+4)}}{\\cancel{9}(a+7)}\\cdot \\dfrac{\\cancel{2}}{\\cancel{2}\\cancel{(3a+4)}}\\Rightarrow \\dfrac{1}{a+7}\\)<\/li>\r\n \t
  18. \\(\\dfrac{k-7}{k^2-k-12}\\cdot \\dfrac{7k^2-28k}{8k^2-56k}\\Rightarrow \\dfrac{\\cancel{k-7}}{\\cancel{(k-4)}(k+3)}\\cdot \\dfrac{7\\cdot \\cancel{k}\\cancel{(k-4)}}{8\\cdot \\cancel{k}\\cancel{(k-7)}}\\Rightarrow \\dfrac{7}{8(k+3)}\\)<\/li>\r\n \t
  19. \\(\\dfrac{x^2-12x+32}{x^2-6x-16}\\cdot \\dfrac{7x^2+14x}{7x^2+21x}\\Rightarrow \\dfrac{\\cancel{(x-8)}(x-4)}{\\cancel{(x-8)}\\cancel{(x+2)}}\\cdot \\dfrac{\\cancel{7x}\\cancel{(x+2)}}{\\cancel{7x}(x+3)}\\Rightarrow \\dfrac{x-4}{x+3}\\)<\/li>\r\n \t
  20. \\(\\dfrac{9x^3+54x^2}{x^2+5x-14}\\cdot \\dfrac{x^2+5x-14}{10x^2}\\Rightarrow \\dfrac{9\\cancel{x^2}(x+6)}{10\\cancel{x^2}}\\Rightarrow \\dfrac{9(x+6)}{10}\\)<\/li>\r\n \t
  21. \\((10m^2+100m)\\cdot \\dfrac{18m^3-36m^2}{20m^2-40m}\\Rightarrow \\cancel{10m}(m+10)\\cdot \\dfrac{\\cancel{2}\\cdot 9m^2\\cancel{(m-2)}}{\\cancel{2}\\cdot \\cancel{10m}\\cancel{(m-2)}}\\Rightarrow\\)\r\n\\(9m^2(m+10)\\)<\/li>\r\n \t
  22. \\(\\dfrac{n-7}{n^2-2n-35}\\div \\dfrac{9n+54}{10n+50}\\Rightarrow \\dfrac{\\cancel{n-7}}{\\cancel{(n-7)}\\cancel{(n+5)}}\\cdot \\dfrac{10\\cancel{(n+5)}}{9(n+6)}\\Rightarrow \\dfrac{10}{9(n+6)}\\)<\/li>\r\n \t
  23. \\(\\\\ \\dfrac{x^2-1}{2x-4}\\cdot \\dfrac{x^2-4}{x^2-x-2}\\div \\dfrac{x^2+x-2}{3x-6}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{\\cancel{(x-1)}\\cancel{(x+1)}}{2\\cancel{(x-2)}}\\cdot \\dfrac{\\cancel{(x+2)}\\cancel{(x-2)}}{\\cancel{(x-2)}\\cancel{(x+1)}}\\cdot \\dfrac{3\\cancel{(x-2)}}{\\cancel{(x+2)}\\cancel{(x-1)}}\\Rightarrow \\dfrac{3}{2}\\)<\/li>\r\n \t
  24. \\(\\dfrac{a^3+b^3}{a^2+3ab+2b^2}\\cdot \\dfrac{3a-6b}{3a^2-3ab+3b^2}\\div \\dfrac{a^2-4b^2}{a+2b}\\Rightarrow \\\\ \\)\r\n\\(\\dfrac{\\cancel{(a+b)}\\cancel{(a^2-ab+b^2)}}{(a+2b)\\cancel{(a+b)}}\\cdot \\dfrac{\\cancel{3}\\cancel{(a-2b)}}{\\cancel{3}\\cancel{(a^2-ab+b^2)}}\\cdot \\dfrac{\\cancel{a+2b}}{\\cancel{(a-2b)}\\cancel{(a+2b)}}\\Rightarrow \\dfrac{1}{a+2b}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\dfrac{8x^2}{9}\cdot \dfrac{9}{2}\Rightarrow \dfrac{\cancel{2}\cdot 4\cdot x^2}{\cancel{9}}\cdot \dfrac{\cancel{9}}{\cancel{2}}\Rightarrow 4x^2\"<\/li>\n
    2. \"\dfrac{8x}{3}\div \dfrac{4x}{7}\Rightarrow \dfrac{8x}{3}\cdot \dfrac{7}{4x} \Rightarrow \dfrac{2\cdot \cancel{4}\cdot \cancel{x}}{3}\cdot \dfrac{7}{\cancel{4}\cdot \cancel{x}}\Rightarrow \dfrac{14}{3}\"<\/li>\n
    3. \"\dfrac{5x^2}{4}\cdot \dfrac{6}{5}\Rightarrow \dfrac{\cancel{5}\cdot x^2}{2\cdot \cancel{2}}\cdot \dfrac{\cancel{2}\cdot 3}{\cancel{5}}\Rightarrow \dfrac{3x^2}{2}\"<\/li>\n
    4. \"\dfrac{10p}{5}\div \dfrac{8}{10}\Rightarrow \dfrac{10p}{5}\cdot \dfrac{10}{8}\Rightarrow \dfrac{\cancel{2}\cdot 5\cdot p}{\cancel{5}}\cdot \dfrac{\cancel{2} \cdot \cancel{5}}{2\cdot \cancel{2} \cdot \cancel{2}}\Rightarrow \dfrac{5p}{2}\"<\/li>\n
    5. \"\dfrac{\cancel{(m-6)}}{7\cancel{(7m-5)}}\cdot \dfrac{5m\cancel{(7m-5)}}{\cancel{m-6}}\Rightarrow \dfrac{5m}{7}\"<\/li>\n
    6. \"\dfrac{7(n-2)}{10(n+3)}\div \dfrac{n-2}{(n+3)}\Rightarrow \dfrac{7\cancel{(n-2)}}{10\cancel{(n+3)}}\cdot \dfrac{\cancel{(n+3)}}{\cancel{n-2}}\Rightarrow \dfrac{7}{10}\"<\/li>\n
    7. \"\dfrac{7r}{7r(r+10)}\div \dfrac{r-6}{(r-6)^2}\Rightarrow \dfrac{7r}{7r(r+10)}\cdot \dfrac{(r-6)^2}{r-6}\Rightarrow \dfrac{\cancel{7r}}{\cancel{7r}(r+10)}\cdot \dfrac{(r-6)\cancel{(r-6)}}{\cancel{r-6}}\Rightarrow \\\"
      \n\"\dfrac{r-6}{r+10}\"<\/li>\n
    8. \"\dfrac{6x(x+4)}{(x-3)}\cdot \dfrac{(x-3)(x-6)}{6x(x-6)}\Rightarrow \dfrac{\cancel{6x}(x+4)}{\cancel{(x-3)}}\cdot \dfrac{\cancel{(x-3)}\cancel{(x-6)}}{\cancel{6x}\cancel{(x-6)}}\Rightarrow x+4\"<\/li>\n
    9. \"\dfrac{x-10}{35x+21}\div \dfrac{7}{35x+21}\Rightarrow \dfrac{x-10}{7\cancel{(5x+3)}}\cdot \dfrac{\cancel{7}\cancel{(5x+3)}}{\cancel{7}}\Rightarrow \dfrac{x-10}{7}\"<\/li>\n
    10. \"\dfrac{v-1}{4}\cdot \dfrac{4}{v^2-11v+10}\Rightarrow \dfrac{\cancel{v-1}}{\cancel{4}}\Rightarrow \dfrac{\cancel{4}}{\cancel{(v-1)}(v-10)}\Rightarrow \dfrac{1}{v-10}\"<\/li>\n
    11. \"\dfrac{x^2-6x-7}{x+5}\cdot \dfrac{x+5}{x-7}\Rightarrow \dfrac{\cancel{(x-7)}(x+1)}{\cancel{(x+5)}}\cdot \dfrac{\cancel{(x+5)}}{\cancel{(x-7)}}\Rightarrow x+1\"<\/li>\n
    12. \"\dfrac{1}{a-6}\cdot \dfrac{8a+80}{8}\Rightarrow \dfrac{1}{a-6}\cdot \dfrac{\cancel{8}(a+10)}{\cancel{8}}\Rightarrow \dfrac{a+10}{a-6}\"<\/li>\n
    13. \"\dfrac{4m+36}{m+9}\cdot \dfrac{m-5}{5m^2}\Rightarrow \dfrac{4\cancel{(m+9)}}{\cancel{m+9}}\cdot \dfrac{m-5}{5m^2}\Rightarrow \dfrac{4(m-5)}{5m^2}\"<\/li>\n
    14. \"\dfrac{2r}{r+6}\div \dfrac{2r}{74+42}\Rightarrow \dfrac{\cancel{2r}}{\cancel{r+6}}\cdot \dfrac{7\cancel{(r+6)}}{\cancel{2r}}\Rightarrow 7\"<\/li>\n
    15. \"\dfrac{n-7}{6n-12}\cdot \dfrac{12-6n}{n^2-13n+42}\Rightarrow \dfrac{\cancel{(n-7)}}{\cancel{6}(n-2)}\cdot \dfrac{\cancel{6}(2-n)}{(n-6)\cancel{(n-7)}}\Rightarrow \dfrac{-1\cancel{(n-2)}}{\cancel{(n-2)}(n-6)}\Rightarrow \\\"
      \n\"\dfrac{-1}{n-6}\"<\/li>\n
    16. \"\dfrac{x^2+11x+24}{6x^3+18x^2}\cdot \dfrac{6x^3+6x^2}{x^2+5x-24}\Rightarrow \dfrac{\cancel{(x+3)}\cancel{(x+8)}}{\cancel{6x^2}\cancel{(x+3)}}\cdot \dfrac{\cancel{6x^2}(x+1)}{\cancel{(x+8)}(x-3)}\Rightarrow \dfrac{x+1}{x-3}\"<\/li>\n
    17. \"\dfrac{27a+36}{9a+63}\div \dfrac{6a+8}{2}\Rightarrow \dfrac{\cancel{9}\cancel{(3a+4)}}{\cancel{9}(a+7)}\cdot \dfrac{\cancel{2}}{\cancel{2}\cancel{(3a+4)}}\Rightarrow \dfrac{1}{a+7}\"<\/li>\n
    18. \"\dfrac{k-7}{k^2-k-12}\cdot \dfrac{7k^2-28k}{8k^2-56k}\Rightarrow \dfrac{\cancel{k-7}}{\cancel{(k-4)}(k+3)}\cdot \dfrac{7\cdot \cancel{k}\cancel{(k-4)}}{8\cdot \cancel{k}\cancel{(k-7)}}\Rightarrow \dfrac{7}{8(k+3)}\"<\/li>\n
    19. \"\dfrac{x^2-12x+32}{x^2-6x-16}\cdot \dfrac{7x^2+14x}{7x^2+21x}\Rightarrow \dfrac{\cancel{(x-8)}(x-4)}{\cancel{(x-8)}\cancel{(x+2)}}\cdot \dfrac{\cancel{7x}\cancel{(x+2)}}{\cancel{7x}(x+3)}\Rightarrow \dfrac{x-4}{x+3}\"<\/li>\n
    20. \"\dfrac{9x^3+54x^2}{x^2+5x-14}\cdot \dfrac{x^2+5x-14}{10x^2}\Rightarrow \dfrac{9\cancel{x^2}(x+6)}{10\cancel{x^2}}\Rightarrow \dfrac{9(x+6)}{10}\"<\/li>\n
    21. \"(10m^2+100m)\cdot \dfrac{18m^3-36m^2}{20m^2-40m}\Rightarrow \cancel{10m}(m+10)\cdot \dfrac{\cancel{2}\cdot 9m^2\cancel{(m-2)}}{\cancel{2}\cdot \cancel{10m}\cancel{(m-2)}}\Rightarrow\"
      \n\"9m^2(m+10)\"<\/li>\n
    22. \"\dfrac{n-7}{n^2-2n-35}\div \dfrac{9n+54}{10n+50}\Rightarrow \dfrac{\cancel{n-7}}{\cancel{(n-7)}\cancel{(n+5)}}\cdot \dfrac{10\cancel{(n+5)}}{9(n+6)}\Rightarrow \dfrac{10}{9(n+6)}\"<\/li>\n
    23. \"\\ \dfrac{x^2-1}{2x-4}\cdot \dfrac{x^2-4}{x^2-x-2}\div \dfrac{x^2+x-2}{3x-6}\Rightarrow \\\"
      \n\"\dfrac{\cancel{(x-1)}\cancel{(x+1)}}{2\cancel{(x-2)}}\cdot \dfrac{\cancel{(x+2)}\cancel{(x-2)}}{\cancel{(x-2)}\cancel{(x+1)}}\cdot \dfrac{3\cancel{(x-2)}}{\cancel{(x+2)}\cancel{(x-1)}}\Rightarrow \dfrac{3}{2}\"<\/li>\n
    24. \"\dfrac{a^3+b^3}{a^2+3ab+2b^2}\cdot \dfrac{3a-6b}{3a^2-3ab+3b^2}\div \dfrac{a^2-4b^2}{a+2b}\Rightarrow \\\"
      \n\"\dfrac{\cancel{(a+b)}\cancel{(a^2-ab+b^2)}}{(a+2b)\cancel{(a+b)}}\cdot \dfrac{\cancel{3}\cancel{(a-2b)}}{\cancel{3}\cancel{(a^2-ab+b^2)}}\cdot \dfrac{\cancel{a+2b}}{\cancel{(a-2b)}\cancel{(a+2b)}}\Rightarrow \dfrac{1}{a+2b}\"<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":70,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1627","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1627","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":3,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1627\/revisions"}],"predecessor-version":[{"id":1630,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1627\/revisions\/1630"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1627\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1627"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1627"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1627"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1627"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}