{"id":3367,"date":"2019-11-19T15:32:40","date_gmt":"2019-11-19T20:32:40","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3367"},"modified":"2019-12-29T20:01:58","modified_gmt":"2019-12-30T01:01:58","slug":"final-exam-version-b-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/final-exam-version-b-answer-key\/","title":{"raw":"Final Exam: Version B Answer Key","rendered":"Final Exam: Version B Answer Key"},"content":{"raw":"[latexpage]\r\n

Questions from Chapters 1 to 3<\/h2>\r\n
    \r\n \t
  1. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-2(-3)-\\sqrt{(-3)^2-4(4)(-1)} \\\\ \\\\\r\n6-\\sqrt{9+16} \\\\ \\\\\r\n6-5 \\\\ \\\\\r\n1\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrrcllll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&18x&-&30&=&3[4&-&4x&-&7] \\\\\r\n&18x&-&30&=&3[-4x&-&3]&& \\\\\r\n&18x&-&30&=&-12x&-&\\phantom{1}9&& \\\\\r\n+&12x&+&30&&+12x&+&30&& \\\\\r\n\\midrule\r\n&&&30x&=&21&&&& \\\\ \\\\\r\n&&&x&=&\\dfrac{21}{30}&=&\\dfrac{7}{10}&&\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{x+4}{2}-\\dfrac{1}{3}=\\dfrac{x+2}{6}\\right)(6) \\\\ \\)\r\n\\(\\begin{array}{rrcrcrrrr}\r\n(x&+&4)(3)&-&1(2)&=&x&+&2 \\\\\r\n3x&+&12&-&2&=&x&+&2 \\\\\r\n-x&-&10&&&&-x&-&10 \\\\\r\n\\midrule\r\n&&&&\\dfrac{2x}{2}&=&\\dfrac{-8}{2}&& \\\\ \\\\\r\n&&&&x&=&-4&&\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&m&=&\\dfrac{\\Delta y}{\\Delta x}&& \\\\ \\\\\r\n&&&&\\dfrac{2}{3}&=&\\dfrac{y-4}{x-1}&& \\\\ \\\\\r\n&&2(x&-&1)&=&3(y&-&4) \\\\\r\n&&2x&-&2&=&3y&-&12 \\\\\r\n&&-3y&+&12&&-3y&+&12 \\\\\r\n\\midrule\r\n2x&-&3y&+&10&=&0&& \\\\ \\\\\r\n&&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{10}{3} \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nd^2&=&\\Delta x^2+\\Delta y^2 \\\\\r\n&=&(4--4)^2+(4--2)^2 \\\\\r\n&=&8^2+6^2 \\\\\r\n&=&64+36 \\\\\r\n&=&100 \\\\ \\\\\r\nd&=&10\r\n\\end{array}\\)<\/li>\r\n \t
  6. \r\n\r\n\r\n\r\n\r\n\r\n
    \\(3x-2y=6\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    2<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n\u22123<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n\u22126<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Line<\/li>\r\n \t
  7. \\(\\begin{array}{rrrcrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n3&\\le &6x&+&3&<&9 \\\\\r\n-3&&&-&3&&-3 \\\\\r\n\\midrule\r\n\\dfrac{0}{6}&\\le &&\\dfrac{6x}{6}&&<&\\dfrac{6}{6} \\\\ \\\\\r\n0&\\le &&x&&<&1\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\n\\((0,1)\\)\r\n\"0,1\"<\/li>\r\n \t
  8. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\left(\\dfrac{3x+1}{4}=2\\right)^4 & \\hspace{0.25in} \\left(\\dfrac{3x+1}{4}=-2\\right)^4 \\\\\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\\r\n3x&+&1&=&8 \\\\\r\n&-&1&&-1 \\\\\r\n\\midrule\r\n&&3x&=&7 \\\\ \\\\\r\n&&x&=&\\dfrac{7}{3}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n3x&+&1&=&-8 \\\\\r\n&-&1&&-1 \\\\\r\n\\midrule\r\n&&3x&=&-9 \\\\\r\n&&x&=&-3\r\n\\end{array}\r\n\\end{array}\\)\r\n\"x=-3,<\/li>\r\n \t
  9. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\hspace{0.75in} w_{\\text{m}}=kw_e \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n&&\\text{1st data} \\\\ \\\\\r\nw_{\\text{m}}&=&38\\text{ lb} \\\\\r\nk&=&\\text{find 1st} \\\\\r\nw_{\\text{e}}&=&95\\text{ lb} \\\\ \\\\\r\nw_{\\text{m}}&=&kw_{\\text{e}} \\\\\r\n38&=&k(95) \\\\ \\\\\r\nk&=&\\dfrac{38}{95} \\\\ \\\\\r\nk&=&0.4\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n&&\\text{2nd data} \\\\ \\\\\r\nw_{\\text{m}}&=&\\text{find} \\\\\r\nk&=&0.4 \\\\\r\nw_{\\text{e}}&=&240\\text{ lb} \\\\ \\\\\r\nw_{\\text{m}}&=&kw_{\\text{e}} \\\\\r\nw_{\\text{m}}&=&(0.4)(240) \\\\\r\nw_{\\text{m}}&=&96\\text{ lb}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\phantom{1}\\)\r\n\\(x, x+2 \\\\ \\)\r\n\\(\\begin{array}{rrrrrrrrrrr}\r\nx&+&x&+&2&=&x&+&2&-&20 \\\\\r\n&&2x&+&2&=&x&-&18&& \\\\\r\n&&-x&-&2&&-x&-&2&& \\\\\r\n\\midrule\r\n&&&&x&=&-20&&&&\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\n\\(\\text{numbers are }-20, -18\\)<\/li>\r\n<\/ol>\r\n

    Questions from Chapters 4 to 6<\/h2>\r\n
      \r\n \t
    1. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(4x&-&3y&=&13)(5) \\\\\r\n&(6x&+&5y&=&-9)(3) \\\\ \\\\\r\n&20x&-&15y&=&\\phantom{-}65 \\\\\r\n+&18x&+&15y&=&-27 \\\\\r\n\\midrule\r\n&&&38x&=&38 \\\\\r\n&&&x&=&1 \\\\ \\\\\r\n&4(1)&-&3y&=&13 \\\\\r\n&-4&&&&-4 \\\\\r\n\\midrule\r\n&&&-3y&=&9 \\\\\r\n&&&y&=&-3\r\n\\end{array}\\)\r\n\\((1,-3)\\)<\/li>\r\n \t
    2. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&x&=&-1-y \\\\ \\\\\r\n\\therefore 3(-1&-&y)&-&4y&=&-5 \\\\\r\n-3&-&3y&-&4y&=&-5 \\\\\r\n+3&&&&&&+3 \\\\\r\n\\midrule\r\n&&&&-7y&=&-2 \\\\\r\n&&&&y&=&\\dfrac{2}{7} \\\\ \\\\\r\n&&x&+&y&=&-1 \\\\\r\n&&x&+&\\dfrac{2}{7}&=&-1 \\\\ \\\\\r\n&&&-&\\dfrac{2}{7}&&-\\dfrac{2}{7} \\\\\r\n\\midrule\r\n&&&&x&=&-\\dfrac{9}{7}\r\n\\end{array}\\)<\/li>\r\n \t
    3. \\(\\begin{array}{rrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&(x&-&4z&=&0)(-1) \\\\ \\\\\r\n&x&+&2y&&&=&0 \\\\\r\n+&-x&&&+&4z&=&0 \\\\\r\n\\midrule\r\n&&&(2y&+&4z&=&0)(\\div 2) \\\\\r\n&&&y&+&2z&=&0 \\\\ \\\\\r\n&&&y&+&2z&=&0 \\\\\r\n&&+&y&-&2z&=&0 \\\\\r\n\\midrule\r\n&&&&&2y&=&0 \\\\\r\n&&&&&y&=&0 \\\\ \\\\\r\n&&&\\cancel{y}0&-&2z&=&0 \\\\\r\n&&&&&z&=&0 \\\\ \\\\\r\n&&&x&+&\\cancel{2y}0&=&0 \\\\\r\n&&&&&x&=&0\r\n\\end{array}\\)\r\n\\((0,0,0)\\)<\/li>\r\n \t
    4. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\\r\n28-\\{5\\cancel{x^0}1-\\cancel{\\left[6x-3(5-2x)\\right]^0}1\\}+5\\cancel{x^0}1 \\\\\r\n28-\\{5-1\\}+5 \\\\\r\n28-4+5 \\\\\r\n29\r\n\\end{array}\\)<\/li>\r\n \t
    5. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&-&3x&+&8\\phantom{x}&& \\\\\r\n\\times&&&x&-&4\\phantom{x}&& \\\\\r\n\\midrule\r\n&x^3&-&3x^2&+&8x&& \\\\\r\n+&&-&4x^2&+&12x&-&32 \\\\\r\n\\midrule\r\n&x^3&-&7x^2&+&20x&-&32 \\\\\r\n\\end{array}\\)<\/li>\r\n \t
    6. \\(\\begin{array}{l}\r\n\\\\ \\\\\r\n(x^{3n-6-3n})^{-1} \\\\\r\n(x^{-6})^{-1} \\\\\r\nx^6\r\n\\end{array}\\)<\/li>\r\n \t
    7. \\(5y(5y^2-3y+1)\\)<\/li>\r\n \t
    8. \\(\\begin{array}{l}\r\n\\\\\r\nx^3+(2y)^3 \\\\\r\n(x+2y)(x^2-2xy+4y^2)\r\n\\end{array}\\)<\/li>\r\n \t
    9. \r\n\r\n\r\n\r\n\r\n\r\n\r\n
      Solution<\/th>\r\nAmount<\/th>\r\nStrength<\/th>\r\nEquation<\/th>\r\n<\/tr>\r\n
      Soda<\/th>\r\n\\(x\\)<\/td>\r\n0<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
      Juice<\/th>\r\n2<\/td>\r\n35<\/td>\r\n2 (35)<\/td>\r\n<\/tr>\r\n
      Diluted<\/th>\r\n\\(x+2\\)<\/td>\r\n8<\/td>\r\n\\((x+2)8\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\\(\\begin{array}{rrrrrl}\r\n&2(35)&=&8(x&+&2) \\\\\r\n&70&=&8x&+&16 \\\\\r\n-&16&&&-&16 \\\\\r\n\\midrule\r\n&54&=&8x&& \\\\ \\\\\r\n&x&=&\\dfrac{54}{8}&\\text{ or }&6\\dfrac{3}{4}\\text{ litres} \\\\\r\n\\end{array}\\)<\/li>\r\n \t
    10. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(d&+&q&=&14)(-10) \\\\\r\n&10d&+&25q&=&185 \\\\ \\\\\r\n&-10d&-&10q&=&-140 \\\\\r\n+&10d&+&25q&=&\\phantom{-}185 \\\\\r\n\\midrule\r\n&&&\\dfrac{15q}{15}&=&\\dfrac{45}{15} \\\\ \\\\\r\n&&&q&=&3 \\\\ \\\\\r\n&\\therefore d&+&3&=&14 \\\\\r\n&&&d&=&11\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n

      Questions from Chapters 7 to 10<\/h2>\r\n
        \r\n \t
      1. \\(\\dfrac{\\cancel{9}\\cancel{s^2}}{7t^3}\\cdot \\dfrac{15\\cancel{t}}{\\cancel{13}\\cancel{s^2}}\\cdot \\dfrac{\\cancel{26}2s}{\\cancel{9}\\cancel{t}}\\Rightarrow \\dfrac{15\\cdot 2\\cdot 5}{7t^3}\\Rightarrow \\dfrac{30s}{7t^3}\\)<\/li>\r\n \t
      2. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{(a-1)2a}{(a-1)(a-6)(a+6)}-\\dfrac{5(a+6)}{(a-6)(a-1)(a+6)} \\Rightarrow \\dfrac{2a^2-2a-5a-30}{(a-1)(a-6)(a+6)} \\\\ \\\\\r\n\\Rightarrow \\dfrac{2a^2-7a-30}{(a-1)(a-6)(a+6)}\\Rightarrow \\dfrac{2a^2-12a+5a-30}{(a-1)(a-6)(a+6)} \\\\ \\\\\r\n\\Rightarrow \\dfrac{2a(a-6)+5(a-6)}{(a-1)(a-6)(a+6)}\\Rightarrow \\dfrac{\\cancel{(a-6)}(2a+5)}{(a-1)\\cancel{(a-6)}(a+6)}\\Rightarrow \\dfrac{2a+5}{(a-1)(a+6)}\r\n\\end{array}\\)<\/li>\r\n \t
      3. \\(\\dfrac{\\left(1-\\dfrac{8}{x}\\right)x^2}{\\left(\\dfrac{3}{x}-\\dfrac{24}{x^2}\\right)x^2}\\Rightarrow \\dfrac{x^2-8x}{3x-24}\\Rightarrow \\dfrac{x\\cancel{(x-8)}}{3\\cancel{(x-8)}}\\Rightarrow \\dfrac{x}{3}\\)<\/li>\r\n \t
      4. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\sqrt{x^4\\cdot x\\cdot y^6\\cdot y}+2xy\\sqrt{16\\cdot x\\cdot y^2\\cdot y}-\\sqrt{x\\cdot y^2\\cdot y} \\\\ \\\\\r\nx^2y^3\\sqrt{xy}+2xy\\cdot 4y\\sqrt{xy}-y\\sqrt{xy} \\\\ \\\\\r\n(x^2y^3+8xy^2-y)\\sqrt{xy}\r\n\\end{array}\\)<\/li>\r\n \t
      5. \\(\\dfrac{2+x}{1-\\sqrt{7}}\\cdot \\dfrac{1+\\sqrt{7}}{1+\\sqrt{7}}\\Rightarrow \\dfrac{2+2\\sqrt{7}+x+x\\sqrt{7}}{1-7}\\Rightarrow \\dfrac{2+x+2\\sqrt{7}+x\\sqrt{7}}{-6}\\)<\/li>\r\n \t
      6. \\(\\left(\\dfrac{a^6b^3}{\\cancel{c^0}1d^{-9}}\\right)^{\\frac{2}{3}}\\Rightarrow \\dfrac{a^{6\\cdot \\frac{2}{3}}b^{3\\cdot \\frac{2}{3}}}{d^{-9\\cdot \\frac{2}{3}}}\\Rightarrow \\dfrac{a^4b^2}{d^{-6}}\\Rightarrow a^4b^2d^6\\)<\/li>\r\n \t
      7. \\(\\begin{array}{rrl}\r\n\\\\\r\n(x-5)(x+3)&=&0 \\\\\r\nx&=&5, -3\r\n\\end{array}\\)<\/li>\r\n \t
      8. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{2x-1}{3x}=\\dfrac{x-3}{x}\\right)(3x) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrrr}\r\n&2x&-&1&=&(x&-&3)(3) \\\\ \\\\\r\n&2x&-&1&=&3x&-&9\\phantom{)(3)} \\\\\r\n+&-3x&+&1&&-3x&+&1\\phantom{)(3)} \\\\\r\n\\midrule\r\n&&&-x&=&-8&& \\\\\r\n&&&x&=&8&&\r\n\\end{array}\\)<\/li>\r\n \t
      9. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nA&=&L\\cdot W \\\\\r\nL&=&5+2W \\\\ \\\\\r\n75&=&W(5+2W) \\\\\r\n75&=&5W+2W^2 \\\\ \\\\\r\n0&=&2W^2+5W-75 \\\\\r\n0&=&2W^2-10W+15W-75 \\\\\r\n0&=&2W(W-5)+15(W-5) \\\\\r\n0&=&(W-5)(2W+15) \\\\\r\nW&=&5, \\cancel{-\\dfrac{15}{2}} \\\\ \\\\\r\nL&=&5+2(5) \\\\\r\nL&=&15\r\n\\end{array}\\)<\/li>\r\n \t
      10. \\(\\phantom{1}\\)\r\n\\(x, x+2, x+4 \\\\ \\)\r\n\\(\\begin{array}{rrcrrrrrrrr}\r\n&&x(x&+&2)&=&8(x&+&4)&-&25 \\\\\r\nx^2&+&2x&&&=&8x&+&32&-&25 \\\\\r\n&-&8x&-&32&&-8x&-&32&+&25 \\\\\r\n&&&+&25&&&&&& \\\\\r\n\\midrule\r\nx^2&-&6x&-&7&=&0&&&& \\\\\r\n(x&-&7)(x&+&1)&=&0&&&& \\\\\r\n&&&&x&=&7,&-1&&& \\\\\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\n\\(\\text{numbers are }7,9,11\\text{ or }-1,1,3\\)<\/li>\r\n<\/ol>","rendered":"

        Questions from Chapters 1 to 3<\/h2>\n
          \n
        1. \"\begin{array}{l}<\/li>\n
        2. \"\begin{array}{rrrrrcllll}<\/li>\n
        3. \"\phantom{1}\"
          \n\"\left(\dfrac{x+4}{2}-\dfrac{1}{3}=\dfrac{x+2}{6}\right)(6) \\\"
          \n\"\begin{array}{rrcrcrrrr}<\/li>\n
        4. \"\begin{array}{rrrrrrrrr}<\/li>\n
        5. \"\begin{array}{rrl}<\/li>\n
        6. \n\n\n\n\n\n\n
          \"3x-2y=6\"<\/caption>\n
          \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
          2<\/td>\n0<\/td>\n<\/tr>\n
          0<\/td>\n\u22123<\/td>\n<\/tr>\n
          \u22122<\/td>\n\u22126<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          \"Line<\/li>\n

        7. \"\begin{array}{rrrcrrr}
          \n\"\phantom{1}\"
          \n\"(0,1)\"
          \n\"0,1\"<\/li>\n
        8. \"\begin{array}{ll}
          \n\"x=-3,<\/li>\n
        9. \"\begin{array}{ll}<\/li>\n
        10. \"\phantom{1}\"
          \n\"x, x+2 \\\"
          \n\"\begin{array}{rrrrrrrrrrr}
          \n\"\phantom{1}\"
          \n\"\text{numbers are }-20, -18\"<\/li>\n<\/ol>\n

          Questions from Chapters 4 to 6<\/h2>\n
            \n
          1. \"\begin{array}{rrrrrl}
            \n\"(1,-3)\"<\/li>\n
          2. \"\begin{array}{rrrrrrl}<\/li>\n
          3. \"\begin{array}{rrrrrrrl}
            \n\"(0,0,0)\"<\/li>\n
          4. \"\begin{array}{l}<\/li>\n
          5. \"\begin{array}{rrrrrrrr}<\/li>\n
          6. \"\begin{array}{l}<\/li>\n
          7. \"5y(5y^2-3y+1)\"<\/li>\n
          8. \"\begin{array}{l}<\/li>\n
          9. \n\n\n\n\n\n\n
            Solution<\/th>\nAmount<\/th>\nStrength<\/th>\nEquation<\/th>\n<\/tr>\n
            Soda<\/th>\n\"x\"<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
            Juice<\/th>\n2<\/td>\n35<\/td>\n2 (35)<\/td>\n<\/tr>\n
            Diluted<\/th>\n\"x+2\"<\/td>\n8<\/td>\n\"(x+2)8\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

            \"\begin{array}{rrrrrl}<\/li>\n

          10. \"\begin{array}{rrrrrl}<\/li>\n<\/ol>\n

            Questions from Chapters 7 to 10<\/h2>\n
              \n
            1. \"\dfrac{\cancel{9}\cancel{s^2}}{7t^3}\cdot \dfrac{15\cancel{t}}{\cancel{13}\cancel{s^2}}\cdot \dfrac{\cancel{26}2s}{\cancel{9}\cancel{t}}\Rightarrow \dfrac{15\cdot 2\cdot 5}{7t^3}\Rightarrow \dfrac{30s}{7t^3}\"<\/li>\n
            2. \"\begin{array}{l}<\/li>\n
            3. \"\dfrac{\left(1-\dfrac{8}{x}\right)x^2}{\left(\dfrac{3}{x}-\dfrac{24}{x^2}\right)x^2}\Rightarrow \dfrac{x^2-8x}{3x-24}\Rightarrow \dfrac{x\cancel{(x-8)}}{3\cancel{(x-8)}}\Rightarrow \dfrac{x}{3}\"<\/li>\n
            4. \"\begin{array}{l}<\/li>\n
            5. \"\dfrac{2+x}{1-\sqrt{7}}\cdot \dfrac{1+\sqrt{7}}{1+\sqrt{7}}\Rightarrow \dfrac{2+2\sqrt{7}+x+x\sqrt{7}}{1-7}\Rightarrow \dfrac{2+x+2\sqrt{7}+x\sqrt{7}}{-6}\"<\/li>\n
            6. \"\left(\dfrac{a^6b^3}{\cancel{c^0}1d^{-9}}\right)^{\frac{2}{3}}\Rightarrow \dfrac{a^{6\cdot \frac{2}{3}}b^{3\cdot \frac{2}{3}}}{d^{-9\cdot \frac{2}{3}}}\Rightarrow \dfrac{a^4b^2}{d^{-6}}\Rightarrow a^4b^2d^6\"<\/li>\n
            7. \"\begin{array}{rrl}<\/li>\n
            8. \"\phantom{1}\"
              \n\"\left(\dfrac{2x-1}{3x}=\dfrac{x-3}{x}\right)(3x) \\\"
              \n\"\begin{array}{rrrrrrrr}<\/li>\n
            9. \"\begin{array}{rrl}<\/li>\n
            10. \"\phantom{1}\"
              \n\"x, x+2, x+4 \\\"
              \n\"\begin{array}{rrcrrrrrrrr}
              \n\"\phantom{1}\"
              \n\"\text{numbers are }7,9,11\text{ or }-1,1,3\"<\/li>\n<\/ol>\n","protected":false},"author":14,"menu_order":112,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-3367","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3367","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\/14"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3367\/revisions"}],"predecessor-version":[{"id":3752,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3367\/revisions\/3752"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3367\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=3367"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=3367"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=3367"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=3367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}