{"id":1661,"date":"2019-07-31T16:19:19","date_gmt":"2019-07-31T20:19:19","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1661"},"modified":"2019-07-31T18:00:24","modified_gmt":"2019-07-31T22:00:24","slug":"answer-key-8-7","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-8-7\/","title":{"raw":"Answer Key 8.7","rendered":"Answer Key 8.7"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&2(x)&&&& \\\\ \\\\\r\n3x(2x)&-&x&-&2&=&0 \\\\\r\n6x^2&-&x&-&2&=&0 \\\\\r\n(3x&-&2)(2x&+&1)&=&0 \\\\ \\\\\r\n&&&&x&=&\\dfrac{2}{3}, -\\dfrac{1}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&x&+&1&& \\\\ \\\\\r\n(x&+&1)(x&+&1)&=&\\phantom{-}4 \\\\\r\nx^2&+&2x&+&1&=&\\phantom{-}4 \\\\\r\n&&&-&4&&-4 \\\\\r\n\\midrule\r\nx^2&+&2x&-&3&=&0 \\\\\r\n(x&-&1)(x&+&3)&=&0 \\\\ \\\\\r\n&&&&x&=&1, -3\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrcrrrllrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&x&-&4&&&&&& \\\\ \\\\\r\nx(x&-&4)&+&20&=&5x&-&2(x&-&4) \\\\\r\nx^2&-&4x&+&20&=&5x&-&2x&+&8 \\\\\r\n&-&3x&-&8&&&-&3x&-&8 \\\\\r\n\\midrule\r\nx^2&-&7x&+&12&=&0&&&& \\\\\r\n(x&-&4)(x&-&3)&=&0&&&& \\\\ \\\\\r\n&&&&x&=&3,&4&&&\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrrrrrrrllr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&x&-&1&&&&&& \\\\ \\\\\r\nx^2&+&6&+&x&-&2&=&\\phantom{-}2x(x&-&1) \\\\\r\n&&x^2&+&x&+&4&=&\\phantom{-}2x^2&-&2x \\\\\r\n&-&2x^2&+&2x&&&&-2x^2&+&2x \\\\\r\n\\midrule\r\n&&-x^2&+&3x&+&4&=&0&& \\\\\r\n&&x^2&-&3x&-&4&=&0&& \\\\\r\n&&(x&-&4)(x&+&1)&=&0&& \\\\ \\\\\r\n&&&&&&x&=&4, 1&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrcrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&x&-&3&& \\\\ \\\\\r\nx(x&-&3)&+&6&=&2x \\\\\r\nx^2&-&3x&+&6&=&2x \\\\\r\n&-&2x&&&&-2x \\\\\r\n\\midrule\r\nx^2&-&5x&+&6&=&0 \\\\\r\n(x&-&3)(x&-&2)&=&0 \\\\ \\\\\r\n&&&&x&=&2, 3\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrcrrrlrrrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x&-&1)(3&-&x)&&&&&&&& \\\\ \\\\\r\n(x&-&4)(3&-&x)&=&\\phantom{-}12(x&-&1)&+&(x&-&1)(3&-&x) \\\\\r\n-x^2&+&7x&-&12&=&\\phantom{-}12x&-&12&-&x^2&+&4x&-&3 \\\\\r\n+x^2&-&16x&+&15&&-12x&+&12&+&x^2&-&4x&+&3 \\\\\r\n\\midrule\r\n&&-9x&+&3&=&0&&&&&&&& \\\\\r\n&&&&3&=&9x&&&&&&&& \\\\ \\\\\r\n&&&&x&=&\\dfrac{3}{9}\\hspace{0.1in}\\text{ or}&\\dfrac{1}{3}&&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrcrcrrrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(2m&-&5)(3m&+&1)(2)&&&&&& \\\\ \\\\\r\n3m(3m&+&1)(2)&-&7(2m&-&5)(2)&=&3(2m&-&5)(3m&+&1) \\\\\r\n18m^2&+&6m&-&28m&+&70&=&18m^2&-&39m&-&15 \\\\\r\n-18m^2&&&+&39m&+&15&&-18m^2&+&39m&+&15 \\\\\r\n\\midrule\r\n&&&&17m&+&85&=&0&&&& \\\\\r\n&&&&&-&85&&-85&&&& \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{17m}{17}&=&\\dfrac{-85}{17}&&&& \\\\ \\\\\r\n&&&&&&m&=&-5&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrcrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(1&-&x)(3&-&x)&& \\\\ \\\\\r\n(4&-&x)(3&-&x)&=&12(1&-&x) \\\\\r\n12&-&7x&+&x^2&=&12&-&12x \\\\\r\n-12&+&12x&&&&-12&+&12x \\\\\r\n\\midrule\r\n&&x^2&+&5x&=&0&& \\\\\r\n&&x(x&+&5)&=&0&& \\\\ \\\\\r\n&&&&x&=&0,&-5&\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{crrrrrcrrrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&2(y&-&3)(y&-&4)&&&&&&&& \\\\ \\\\\r\n7(2)(y&-&4)&-&1(y&-&3)(y&-&4)&=&(y&-&2)(2)(y&-&3) \\\\\r\n14y&-&56&-&y^2&+&7y&-&12&=&2y^2&-&10y&+&12 \\\\ \\\\\r\n&&&&-\\phantom{0}y^2&+&21y&-&68&=&2y^2&-&10y&+&12 \\\\\r\n&&&&-2y^2&+&10y&-&12&&-2y^2&+&10y&-&12 \\\\\r\n\\midrule\r\n&&&&-3y^2&+&31y&-&80&=&0&&&& \\\\\r\n&&&&3y^2&-&31y&+&80&=&0&&&& \\\\\r\n&&&&(y&-&5)(3y&-&16)&=&0&&&& \\\\ \\\\\r\n&&&&&&&&y&=&5, &\\dfrac{16}{3}&&&\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x&+&2)(x&-&2)&&&& \\\\ \\\\\r\n1(x&-&2)&+&1(x&+&2)&=&3x&+&8 \\\\\r\nx&-&2&+&x&+&2&=&3x&+&8 \\\\\r\n&&&&-2x&&&&-2x&& \\\\\r\n\\midrule\r\n&&&&&&0&=&x&+&8 \\\\\r\n&&&&&&-8&&&-&8 \\\\\r\n\\midrule\r\n&&&&&&x&=&-8&&\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrcrcrrrcrcrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x&+&1)(x&-&1)(6)&&&&&&&&&& \\\\ \\\\\r\n(x&+&1)(x&+&1)(6)&-&(x&-&1)(x&-&1)(6)&=&5(x&+&1)(x&-&1) \\\\\r\n6(x^2&+&2x&+&1)&-&6(x^2&-&2x&+&1)&=&5(x^2&&-&&1) \\\\\r\n6x^2&+&12x&+&6&-&6x^2&+&12x&-&6&=&5x^2&&&-&5 \\\\\r\n&&&&&&&&&&24x&=&5x^2&&&-&5 \\\\\r\n&&&&&&&&&&-24x&&&-&24x&& \\\\\r\n\\midrule\r\n&&&&&&&&&&0&=&5x^2&-&24x&-&5 \\\\\r\n&&&&&&&&&&0&=&(5x&+&1)(x&-&5) \\\\ \\\\\r\n&&&&&&&&&&x&=&5, &-\\dfrac{1}{5}&&&\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrcrcrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x&+&3)(x&-&2)&&&& \\\\ \\\\\r\n(x&-&2)(x&-&2)&-&1(x&+&3)&=&1 \\\\\r\nx^2&-&4x&+&4&-&x&-&3&=&1 \\\\\r\n&&&&&&&-&1&&-1 \\\\\r\n\\midrule\r\n&&&&&&x^2&-&5x&=&0 \\\\\r\n&&&&&&x(x&-&5)&=&0 \\\\ \\\\\r\n&&&&&&&&x&=&0, 5\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrcrrrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x&-&1)(x&+&1)&&&&&& \\\\ \\\\\r\nx(x&+&1)&-&2(x&-&1)&=&4x^2&&&& \\\\\r\nx^2&+&x&-&2x&+&2&=&4x^2&&&& \\\\\r\n-x^2&&&+&x&-&2&&-x^2&+&x&-&2 \\\\\r\n\\midrule\r\n&&&&&&0&=&3x^2&+&x&-&2 \\\\\r\n&&&&&&0&=&(3x&-&2)(x&+&1) \\\\ \\\\\r\n&&&&&&0&=&\\dfrac{2}{3},&-1&&&\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrcrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x&+&2)(x&-&4)&& \\\\ \\\\\r\n2x(x&-&4)&+&2(x&+&2)&=&3x \\\\\r\n2x^2&-&8x&+&2x&+&4&=&3x \\\\\r\n&&&-&3x&&&&-3x \\\\\r\n\\midrule\r\n&&2x^2&-&9x&+&4&=&0 \\\\\r\n&&(2x&-&1)(x&-&4)&=&0 \\\\ \\\\\r\n&&&&&&x&=&\\dfrac{1}{2}, 4\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{LCD}&=&(x&+&1)(x&+&5)&& \\\\ \\\\\r\n2x(x&+&5)&-&3(x&+&1)&=&-8x^2 \\\\\r\n2x^2&+&10x&-&3x&-&3&=&-8x^2 \\\\\r\n+8x^2&&&&&&&&+8x^2 \\\\\r\n\\midrule\r\n&&10x^2&+&7x&-&3&=&0 \\\\\r\n&&(10x&-&3)(x&+&1)&=&0 \\\\ \\\\\r\n&&&&&&x&=&\\dfrac{3}{10}, -1\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
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