{"id":1938,"date":"2021-12-02T19:40:05","date_gmt":"2021-12-03T00:40:05","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-1\/"},"modified":"2022-11-02T10:38:33","modified_gmt":"2022-11-02T14:38:33","slug":"answer-key-8-1","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-1\/","title":{"raw":"Answer Key 8.1","rendered":"Answer Key 8.1"},"content":{"raw":"
    \n \t
  1. [latex]\\dfrac{4(4)+2}{6}\\Rightarrow \\dfrac{16+2}{6}\\Rightarrow \\dfrac{18}{6}\\Rightarrow 3[\/latex]<\/li>\n \t
  2. [latex]\\dfrac{-2-3}{3(-2)-9}\\Rightarrow \\dfrac{-5}{-6-9}\\Rightarrow \\dfrac{-5}{-15}\\Rightarrow \\dfrac{1}{3}[\/latex]<\/li>\n \t
  3. [latex]\\dfrac{-4-3}{(-4)^2-4(-4)+3}\\Rightarrow \\dfrac{-7}{16+16+3}\\Rightarrow -\\dfrac{7}{35}\\Rightarrow -\\dfrac{1}{5}[\/latex]<\/li>\n \t
  4. [latex]\\dfrac{-1+2}{(-1)^2+3(-1)+2}\\Rightarrow \\dfrac{1}{1-3+2}\\Rightarrow \\dfrac{1}{0}\\Rightarrow \\text{Undefined}[\/latex]<\/li>\n \t
  5. [latex]\\dfrac{\\cancel{b}+2}{\\cancel{b^2+4b}+4}\\Rightarrow \\dfrac{2}{4}\\Rightarrow \\dfrac{1}{2}[\/latex]<\/li>\n \t
  6. [latex]\\dfrac{(4)^2-4-6}{4-3}\\Rightarrow \\dfrac{16-10}{1}\\Rightarrow \\dfrac{6}{1} \\Rightarrow 6[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\nk&+&10&\\neq &0 \\\\\n&-&10&&-10 \\\\\n\\hline\n&&k&\\neq &-10\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n&&18p(p&-&2) \\\\ \\\\\n&&18p&\\neq &0 \\\\\n&&p&\\neq &0 \\\\ \\\\\np&-&2&\\neq &0 \\\\\n&+&2&&+2 \\\\\n\\hline\n&&p&\\neq &2\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]10m\\neq 0[\/latex]\n[latex]m\\neq 0[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]2(3x+10)\\Rightarrow \\begin{array}[t]{rrrrr}\n3x&+&10&\\neq &0 \\\\\n&-&10&&-10 \\\\\n\\hline\n&&3x&\\neq &-10 \\\\ \\\\\n&&x&\\neq &-\\dfrac{10}{3}\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]5(r+2)[\/latex]\n[latex]r\\neq -2[\/latex]<\/li>\n \t
  12. [latex]3n(2n+1)[\/latex]\n[latex]\\begin{array}[t]{rrr}\nn&\\neq &0 \\\\ \\\\\nn&\\neq &-\\dfrac{1}{2}\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex](b-4)(b+8)[\/latex]\n[latex]\\begin{array}[t]{rrr}\nb&\\neq &4 \\\\\nb&\\neq &-8\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]5v(7v-1)[\/latex]\n[latex]\\begin{array}[t]{rrr}\nv&\\neq &0 \\\\\nv&\\neq &\\dfrac{1}{7}\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\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}[\/latex]<\/li>\n \t
  16. [latex]\\dfrac{12n}{4n^2}\\Rightarrow \\dfrac{3\\cdot \\cancel{4}\\cdot \\cancel{n}}{\\cancel{4}\\cdot \\cancel{n}\\cdot n}\\Rightarrow \\dfrac{3}{n}[\/latex]<\/li>\n \t
  17. [latex]\\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}[\/latex]<\/li>\n \t
  18. [latex]\\dfrac{21k}{24k^2}\\Rightarrow \\dfrac{\\cancel{3}\\cdot 7\\cdot \\cancel{k}}{\\cancel{3}\\cdot 8\\cdot k}\\Rightarrow \\dfrac{7}{8k}[\/latex]<\/li>\n \t
  19. [latex]\\dfrac{18m-24}{60}\\Rightarrow \\dfrac{\\cancel{6}(3m-4)}{\\cancel{6}(10)}\\Rightarrow \\dfrac{3m-4}{10}[\/latex]<\/li>\n \t
  20. [latex]\\dfrac{n-9}{9n-81}\\Rightarrow \\dfrac{\\cancel{n-9}}{9\\cancel{(n-9)}}\\Rightarrow \\dfrac{1}{9}[\/latex]<\/li>\n \t
  21. [latex]\\dfrac{x+1}{x^2+8x+7}\\Rightarrow \\dfrac{\\cancel{x+1}}{\\cancel{(x+1)}(x+7)}\\Rightarrow \\dfrac{1}{x+7}[\/latex]<\/li>\n \t
  22. [latex]\\dfrac{28m+12}{36}\\Rightarrow \\dfrac{\\cancel{4}(7m+3)}{\\cancel{4}(9)}\\Rightarrow \\dfrac{7m+3}{9}[\/latex]<\/li>\n \t
  23. [latex]\\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}[\/latex]<\/li>\n \t
  24. [latex]\\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}[\/latex]<\/li>\n \t
  25. [latex]\\dfrac{9v+54}{v^2-4v-60}\\Rightarrow \\dfrac{9\\cancel{(v-6)}}{(v-10)\\cancel{(v+6)}}\\Rightarrow \\dfrac{9}{v-10}[\/latex]<\/li>\n \t
  26. [latex]\\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}[\/latex]<\/li>\n \t
  27. [latex]\\dfrac{2n^2+19n-10}{9n+90}\\Rightarrow \\dfrac{(2n-1)\\cancel{(n+10)}}{9\\cancel{(n+10)}}\\Rightarrow \\dfrac{2n-1}{9}[\/latex]<\/li>\n \t
  28. [latex]\\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)}[\/latex]<\/li>\n \t
  29. [latex]\\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}[\/latex]<\/li>\n \t
  30. [latex]\\dfrac{7n^2-32n+16}{4n-16}\\Rightarrow \\dfrac{(7n-4)\\cancel{(n-4)}}{4\\cancel{(n-4)}}\\Rightarrow \\dfrac{7n-4}{4}[\/latex]<\/li>\n \t
  31. [latex]\\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)}[\/latex]<\/li>\n \t
  32. [latex]\\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}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\dfrac{4(4)+2}{6}\\Rightarrow \\dfrac{16+2}{6}\\Rightarrow \\dfrac{18}{6}\\Rightarrow 3[\/latex]<\/li>\n
    2. [latex]\\dfrac{-2-3}{3(-2)-9}\\Rightarrow \\dfrac{-5}{-6-9}\\Rightarrow \\dfrac{-5}{-15}\\Rightarrow \\dfrac{1}{3}[\/latex]<\/li>\n
    3. [latex]\\dfrac{-4-3}{(-4)^2-4(-4)+3}\\Rightarrow \\dfrac{-7}{16+16+3}\\Rightarrow -\\dfrac{7}{35}\\Rightarrow -\\dfrac{1}{5}[\/latex]<\/li>\n
    4. [latex]\\dfrac{-1+2}{(-1)^2+3(-1)+2}\\Rightarrow \\dfrac{1}{1-3+2}\\Rightarrow \\dfrac{1}{0}\\Rightarrow \\text{Undefined}[\/latex]<\/li>\n
    5. [latex]\\dfrac{\\cancel{b}+2}{\\cancel{b^2+4b}+4}\\Rightarrow \\dfrac{2}{4}\\Rightarrow \\dfrac{1}{2}[\/latex]<\/li>\n
    6. [latex]\\dfrac{(4)^2-4-6}{4-3}\\Rightarrow \\dfrac{16-10}{1}\\Rightarrow \\dfrac{6}{1} \\Rightarrow 6[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} k&+&10&\\neq &0 \\\\ &-&10&&-10 \\\\ \\hline &&k&\\neq &-10 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} &&18p(p&-&2) \\\\ \\\\ &&18p&\\neq &0 \\\\ &&p&\\neq &0 \\\\ \\\\ p&-&2&\\neq &0 \\\\ &+&2&&+2 \\\\ \\hline &&p&\\neq &2 \\end{array}[\/latex]<\/li>\n
    9. [latex]10m\\neq 0[\/latex]
      \n[latex]m\\neq 0[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]2(3x+10)\\Rightarrow \\begin{array}[t]{rrrrr} 3x&+&10&\\neq &0 \\\\ &-&10&&-10 \\\\ \\hline &&3x&\\neq &-10 \\\\ \\\\ &&x&\\neq &-\\dfrac{10}{3} \\end{array}[\/latex]<\/li>\n
    11. [latex]5(r+2)[\/latex]
      \n[latex]r\\neq -2[\/latex]<\/li>\n
    12. [latex]3n(2n+1)[\/latex]
      \n[latex]\\begin{array}[t]{rrr} n&\\neq &0 \\\\ \\\\ n&\\neq &-\\dfrac{1}{2} \\end{array}[\/latex]<\/li>\n
    13. [latex](b-4)(b+8)[\/latex]
      \n[latex]\\begin{array}[t]{rrr} b&\\neq &4 \\\\ b&\\neq &-8 \\end{array}[\/latex]<\/li>\n
    14. [latex]5v(7v-1)[\/latex]
      \n[latex]\\begin{array}[t]{rrr} v&\\neq &0 \\\\ v&\\neq &\\dfrac{1}{7} \\end{array}[\/latex]<\/li>\n
    15. [latex]\\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}[\/latex]<\/li>\n
    16. [latex]\\dfrac{12n}{4n^2}\\Rightarrow \\dfrac{3\\cdot \\cancel{4}\\cdot \\cancel{n}}{\\cancel{4}\\cdot \\cancel{n}\\cdot n}\\Rightarrow \\dfrac{3}{n}[\/latex]<\/li>\n
    17. [latex]\\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}[\/latex]<\/li>\n
    18. [latex]\\dfrac{21k}{24k^2}\\Rightarrow \\dfrac{\\cancel{3}\\cdot 7\\cdot \\cancel{k}}{\\cancel{3}\\cdot 8\\cdot k}\\Rightarrow \\dfrac{7}{8k}[\/latex]<\/li>\n
    19. [latex]\\dfrac{18m-24}{60}\\Rightarrow \\dfrac{\\cancel{6}(3m-4)}{\\cancel{6}(10)}\\Rightarrow \\dfrac{3m-4}{10}[\/latex]<\/li>\n
    20. [latex]\\dfrac{n-9}{9n-81}\\Rightarrow \\dfrac{\\cancel{n-9}}{9\\cancel{(n-9)}}\\Rightarrow \\dfrac{1}{9}[\/latex]<\/li>\n
    21. [latex]\\dfrac{x+1}{x^2+8x+7}\\Rightarrow \\dfrac{\\cancel{x+1}}{\\cancel{(x+1)}(x+7)}\\Rightarrow \\dfrac{1}{x+7}[\/latex]<\/li>\n
    22. [latex]\\dfrac{28m+12}{36}\\Rightarrow \\dfrac{\\cancel{4}(7m+3)}{\\cancel{4}(9)}\\Rightarrow \\dfrac{7m+3}{9}[\/latex]<\/li>\n
    23. [latex]\\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}[\/latex]<\/li>\n
    24. [latex]\\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}[\/latex]<\/li>\n
    25. [latex]\\dfrac{9v+54}{v^2-4v-60}\\Rightarrow \\dfrac{9\\cancel{(v-6)}}{(v-10)\\cancel{(v+6)}}\\Rightarrow \\dfrac{9}{v-10}[\/latex]<\/li>\n
    26. [latex]\\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}[\/latex]<\/li>\n
    27. [latex]\\dfrac{2n^2+19n-10}{9n+90}\\Rightarrow \\dfrac{(2n-1)\\cancel{(n+10)}}{9\\cancel{(n+10)}}\\Rightarrow \\dfrac{2n-1}{9}[\/latex]<\/li>\n
    28. [latex]\\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)}[\/latex]<\/li>\n
    29. [latex]\\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}[\/latex]<\/li>\n
    30. [latex]\\dfrac{7n^2-32n+16}{4n-16}\\Rightarrow \\dfrac{(7n-4)\\cancel{(n-4)}}{4\\cancel{(n-4)}}\\Rightarrow \\dfrac{7n-4}{4}[\/latex]<\/li>\n
    31. [latex]\\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)}[\/latex]<\/li>\n
    32. [latex]\\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}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":74,"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-1938","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\/1938","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\/1938\/revisions"}],"predecessor-version":[{"id":1939,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1938\/revisions\/1939"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1938\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1938"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1938"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1938"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}