{"id":1600,"date":"2019-07-26T18:55:49","date_gmt":"2019-07-26T22:55:49","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1600"},"modified":"2019-07-29T12:25:08","modified_gmt":"2019-07-29T16:25:08","slug":"answer-key-7-8","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-7-8\/","title":{"raw":"Answer Key 7.8","rendered":"Answer Key 7.8"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rr}\r\n\\\\ \\\\\r\n\\begin{array}{rrrrr}\r\nk&-&7&=&0 \\\\\r\n&+&7&&+7 \\\\\r\n\\midrule\r\n&&k&=&7\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\nk&+&2&=&0 \\\\\r\n&-&2&&-2 \\\\\r\n\\midrule\r\n&&k&=&-2\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rr}\r\n\\\\ \\\\\r\n\\begin{array}{rrrrr}\r\na&+&4&=&0 \\\\\r\n&-&4&&-4 \\\\\r\n\\midrule\r\n&&a&=&-4\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\na&-&3&=&0 \\\\\r\n&+&3&&+3 \\\\\r\n\\midrule\r\n&&a&=&3\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rr}\r\n\\\\ \\\\\r\n\\begin{array}{rrrrr}\r\nx&-&1&=&0 \\\\\r\n&+&1&&+1 \\\\\r\n\\midrule\r\n&&x&=&1\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\nx&+&4&=&0 \\\\\r\n&-&4&&-4 \\\\\r\n\\midrule\r\n&&x&=&-4\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rr}\r\n\\\\ \\\\\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\\r\n2x&+&5&=&0 \\\\\r\n&-&5&&-5 \\\\\r\n\\midrule\r\n&&\\dfrac{2x}{2}&=&\\dfrac{-5}{2} \\\\ \\\\\r\n&&x&=&-\\dfrac{5}{2}\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\nx&-&7&=&0 \\\\\r\n&+&7&&+7 \\\\\r\n\\midrule\r\n&&x&=&7\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n6(x^2-25)&=&0 \\\\\r\n6(x-5)(x+5)&=&0 \\\\ \\\\\r\nx&=&5 \\\\\r\nx&=&-5\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrr}\r\n\\\\ \\\\ \\\\\r\n(p+8)(p-4)&=&0 \\\\ \\\\\r\np&=&-8 \\\\\r\np&=&4\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n2(n^2+5n-14)&=&0 \\\\\r\n2(n+7)(n-2)&=&0 \\\\ \\\\\r\nn&=&-7 \\\\\r\nn&=&2\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrr}\r\n\\\\ \\\\ \\\\\r\n(m-6)(m+5)&=&0 \\\\ \\\\\r\nm&=&6 \\\\\r\nm&=&-5\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n(x+3)(7x+5)&=&0 \\\\ \\\\\r\nx&=&-3 \\\\\r\nx&=&-\\dfrac{5}{7}\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n(2b+1)(b-2)&=&0 \\\\ \\\\\r\nb&=&-\\dfrac{1}{2} \\\\ \\\\\r\nb&=&2\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx^2&-&4x&-&8&=&-8 \\\\\r\n&&&+&8&&+8 \\\\\r\n\\midrule\r\n&&x^2&-&4x&=&0 \\\\\r\n&&x(x&-&4)&=&0 \\\\ \\\\\r\n&&&&x&=&0 \\\\\r\n&&&&x&=&4\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nv^2&-&8v&-&3&=&-3 \\\\\r\n&&&+&3&&+3 \\\\\r\n\\midrule\r\n&&v^2&-&8v&=&0 \\\\\r\n&&v(v&-&8)&=&0 \\\\ \\\\\r\n&&&&v&=&0 \\\\\r\n&&&&v&=&8\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&-&5x&-&1&=&-5 \\\\\r\n&&&&+&5&&+5 \\\\\r\n\\midrule\r\n&x^2&-&5x&+&4&=&0 \\\\\r\n(x&-&4)&(x&-&1)&=&0 \\\\ \\\\\r\n&&&&&x&=&4 \\\\\r\n&&&&&x&=&1\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&a^2&-&6a&+&6&=&-2 \\\\\r\n&&&&+&2&=&+2 \\\\\r\n\\midrule\r\n&a^2&-&6a&+&8&=&0 \\\\\r\n(a&-&4)&(a&-&2)&=&0 \\\\ \\\\\r\n&&&&&a&=&4 \\\\\r\n&&&&&a&=&2\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&7x^2&+&17x&-&20&=&-8 \\\\\r\n&&&&+&8&&+8 \\\\\r\n\\midrule\r\n&7x^2&+&17x&-&12&=&0 \\\\\r\n(7x&-&4)&(x&+&3)&=&0 \\\\ \\\\\r\n&&&&&x&=&\\dfrac{4}{7} \\\\ \\\\\r\n&&&&&x&=&-3\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&4n^2&-&13n&+&8&=&5 \\\\\r\n&&&&-&5&&-5 \\\\\r\n\\midrule\r\n&4n^2&-&13n&+&3&=&0 \\\\\r\n(4n&-&1)&(n&-&3)&=&0 \\\\ \\\\\r\n&&&&&n&=&\\dfrac{1}{4} \\\\ \\\\\r\n&&&&&n&=&3\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&-&6x&&&=&16 \\\\\r\n&&&&-&16&&-16 \\\\\r\n\\midrule\r\n&x^2&-&6x&-&16&=&0 \\\\\r\n(x&-&8)&(x&+&2)&=&0 \\\\ \\\\\r\n&&&&&x&=&8 \\\\\r\n&&&&&x&=&-2 \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n7n^2&-&28n&=&0 \\\\\r\n7n(n&-&4)&=&0 \\\\ \\\\\r\n&&n&=&0 \\\\\r\n&&n&=&4\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rcrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&4k^2&+&22k&+&23&=&6k&+&7 \\\\\r\n&&-&6k&-&7&&-6k&-&7 \\\\\r\n\\midrule\r\n&4k^2&+&16k&+&16&=&0&& \\\\\r\n&4(k^2&+&4k&+&4)&=&0&& \\\\\r\n4(k&+&2)&(k&+&2)&=&0&& \\\\ \\\\\r\n&&&&&k&=&-2&&\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&a^2&+&7a&-&9&=&-3&+&6a \\\\\r\n&&-&6a&+&3&&+3&-&6a \\\\\r\n\\midrule\r\n&a^2&+&a&-&6&=&0&& \\\\\r\n(a&+&3)&(a&-&2)&=&0&& \\\\ \\\\\r\n&&&&&a&=&-3&& \\\\\r\n&&&&&a&=&2&&\r\n\\end{array}\\)<\/li>\r\n \t
  21. \\(\\begin{array}{rrrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&9x^2&-&46&+&7x&=&7x&+&8x^2&+&3 \\\\\r\n&-8x^2&-&3&-&7x&&-7x&-&8x^2&-&3 \\\\\r\n\\midrule\r\n&&&x^2&-&49&=&0&&&& \\\\\r\n(x&-&7)&(x&+&7)&=&0&&&& \\\\ \\\\\r\n&&&&&x&=&7&&&& \\\\\r\n&&&&&x&=&-7&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&+&10x&+&30&=&6 \\\\\r\n&&&&-&6&=&-6 \\\\\r\n\\midrule\r\n&x^2&+&10x&+&24&=&0 \\\\\r\n(x&+&6)&(x&+&4)&=&0 \\\\ \\\\\r\n&&&&&x&=&-6 \\\\\r\n&&&&&x&=&-4\r\n\\end{array}\\)<\/li>\r\n \t
  23. \\(\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&40p^2&+&183p&-&168&=&p&+&5p^2 \\\\\r\n&-5p^2&-&p&&&&-p&-&5p^2 \\\\\r\n\\midrule\r\n&35p^2&+&182p&-&168&=&0&& \\\\\r\n&7(5p^2&+&26p&-&24)&=&0&& \\\\\r\n7(p&+&6)&(5p&-&4)&=&0&& \\\\ \\\\\r\n&&&&&p&=&-6&& \\\\ \\\\\r\n&&&&&p&=&\\dfrac{4}{5}&&\r\n\\end{array}\\)<\/li>\r\n \t
  24. \\(\\begin{array}{rcrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&24x^2&+&11x&-&80&=&3x \\\\\r\n&&-&3x&&&&-3x \\\\\r\n\\midrule\r\n&24x^2&+&8x&-&80&=&0 \\\\\r\n&8(3x^2&+&x&-&10)&=&0 \\\\\r\n8(3x&-&5)&(x&+&2)&=&0 \\\\ \\\\\r\n&&&&&x&=&\\dfrac{5}{3} \\\\ \\\\\r\n&&&&&x&=&-2\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
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