{"id":1948,"date":"2021-12-02T19:40:08","date_gmt":"2021-12-03T00:40:08","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-6\/"},"modified":"2022-11-02T10:38:38","modified_gmt":"2022-11-02T14:38:38","slug":"answer-key-8-6","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-8-6\/","title":{"raw":"Answer Key 8.6","rendered":"Answer Key 8.6"},"content":{"raw":"
    \n \t
  1. [latex]\\text{LCD}=5(2)[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n2(m&-&1)&=&5(8) \\\\\n2m&-&2&=&40 \\\\\n&+&2&&+2 \\\\\n\\hline\n&&\\dfrac{2m}{2}&=&\\dfrac{42}{2} \\\\ \\\\\n&&m&=&21\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\text{LCD}=2(x-8)[\/latex]\n[latex]\\begin{array}[t]{rrrrl}\n8(x&-&8)&=&\\phantom{+}2(8) \\\\\n8x&-&64&=&\\phantom{+}16 \\\\\n&+&64&&+64 \\\\\n\\hline\n&&\\dfrac{8x}{8}&=&\\phantom{+}\\dfrac{80}{8} \\\\ \\\\\n&&x&=&\\phantom{+}10\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\text{LCD}=9(p-4)[\/latex]\n[latex]\\begin{array}[t]{rrrrl}\n2(p&-&4)&=&9(10) \\\\\n2p&-&8&=&90 \\\\\n&+&8&&+8 \\\\\n\\hline\n&&\\dfrac{2p}{2}&=&\\dfrac{98}{2} \\\\ \\\\\n&&p&=&49\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\text{LCD}=9(n+2)[\/latex]\n[latex]\\begin{array}[t]{rllll}\n9(9)&=&3(n&+&2) \\\\\n81&=&3n&+&6 \\\\\n-6&&&-&6 \\\\\n\\hline\n\\dfrac{75}{3}&=&\\dfrac{3n}{3}&& \\\\ \\\\\nn&=&25&&\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]\\text{LCD}=10(a+2)[\/latex]\n[latex]\\begin{array}[t]{rrlrl}\n3(a&+&2)&=&10(a) \\\\\n3a&+&6&=&10a \\\\\n-3a&&&&-3a \\\\\n\\hline\n&&\\dfrac{6}{7}&=&\\dfrac{7a}{7} \\\\ \\\\\n&&a&=&\\dfrac{6}{7}\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]\\text{LCD}=3(4)[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n4(x&+&1)&=&3(x&+&3) \\\\\n4x&+&4&=&3x&+&9 \\\\\n-3x&-&4&&-3x&-&4 \\\\\n\\hline\n&&x&=&5&&\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\text{LCD}=3(p+4)[\/latex]\n[latex]\\begin{array}[t]{rrrrcrr}\n2(3)&=&(p&+&4)(p&+&5) \\\\\n6&=&p^2&+&9p&+&20 \\\\\n-6&&&&&-&6 \\\\\n\\hline\n0&=&p^2&+&9p&+&14 \\\\\n0&=&(p&+&7)(p&+&2) \\\\ \\\\\np&=&-2,&-7&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\text{LCD}=10(n+1)[\/latex]\n[latex]\\begin{array}[t]{rrrrcrr}\n5(10)&=&(n&-&4)(n&+&1) \\\\\n50&=&n^2&-&3n&-&4 \\\\\n-50&&&&&-&50 \\\\\n\\hline\n0&=&n^2&-&3n&-&54 \\\\\n0&=&(n&-&9)(n&+&6) \\\\ \\\\\nn&=&9,&-6&&&\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\text{LCD}=5(x-2)[\/latex]\n[latex]\\begin{array}[t]{rrcrrrl}\n(x&+&5)(x&-&2)&=&5(6) \\\\\nx^2&+&3x&-&10&=&\\phantom{-}30 \\\\\n&&&-&30&&-30 \\\\\n\\hline\nx^2&+&3x&-&40&=&0 \\\\\n(x&-&5)(x&+&8)&=&0 \\\\ \\\\\n&&&&x&=&5, -7\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\text{LCD}=5(x-3)[\/latex]\n[latex]\\begin{array}[t]{rrrrcrr}\n20&=&(x&-&3)(x&+&5) \\\\\n20&=&x^2&+&2x&-&15 \\\\\n-20&&&&&-&20 \\\\\n\\hline\n0&=&x^2&+&2x&-&35 \\\\\n0&=&(x&-&5)(x&+&7) \\\\ \\\\\nx&=&5,&-7&&&\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\text{LCD}=4(m-4)[\/latex]\n[latex]\\begin{array}[t]{rrcrrrl}\n(m&+&3)(m&-&4)&=&4(11) \\\\\nm^2&-&m&-&12&=&\\phantom{-}44 \\\\\n&&&-&44&&-44 \\\\\n\\hline\n(m^2&-&m&-&56)&=&0 \\\\\n(m&-&8)(m&+&7)&=&0 \\\\ \\\\\n&&&&m&=&8, -7\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\text{LCD}=8(x-1)[\/latex]\n[latex]\\begin{array}[t]{rrcrrrl}\n(x&-&5)(x&-&1)&=&4(8) \\\\\nx^2&-&6x&+&5&=&\\phantom{-}32 \\\\\n&&&-&32&&-32 \\\\\n\\hline\nx^2&-&6x&-&27&=&0 \\\\\n(x&-&9)(x&+&3)&=&0 \\\\ \\\\\n&&&&x&=&9, -3\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\text{LCD}=5(2)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 2(m&-&1)&=&5(8) \\\\ 2m&-&2&=&40 \\\\ &+&2&&+2 \\\\ \\hline &&\\dfrac{2m}{2}&=&\\dfrac{42}{2} \\\\ \\\\ &&m&=&21 \\end{array}[\/latex]<\/li>\n
    2. [latex]\\text{LCD}=2(x-8)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} 8(x&-&8)&=&\\phantom{+}2(8) \\\\ 8x&-&64&=&\\phantom{+}16 \\\\ &+&64&&+64 \\\\ \\hline &&\\dfrac{8x}{8}&=&\\phantom{+}\\dfrac{80}{8} \\\\ \\\\ &&x&=&\\phantom{+}10 \\end{array}[\/latex]<\/li>\n
    3. [latex]\\text{LCD}=9(p-4)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrl} 2(p&-&4)&=&9(10) \\\\ 2p&-&8&=&90 \\\\ &+&8&&+8 \\\\ \\hline &&\\dfrac{2p}{2}&=&\\dfrac{98}{2} \\\\ \\\\ &&p&=&49 \\end{array}[\/latex]<\/li>\n
    4. [latex]\\text{LCD}=9(n+2)[\/latex]
      \n[latex]\\begin{array}[t]{rllll} 9(9)&=&3(n&+&2) \\\\ 81&=&3n&+&6 \\\\ -6&&&-&6 \\\\ \\hline \\dfrac{75}{3}&=&\\dfrac{3n}{3}&& \\\\ \\\\ n&=&25&& \\end{array}[\/latex]<\/li>\n
    5. [latex]\\text{LCD}=10(a+2)[\/latex]
      \n[latex]\\begin{array}[t]{rrlrl} 3(a&+&2)&=&10(a) \\\\ 3a&+&6&=&10a \\\\ -3a&&&&-3a \\\\ \\hline &&\\dfrac{6}{7}&=&\\dfrac{7a}{7} \\\\ \\\\ &&a&=&\\dfrac{6}{7} \\end{array}[\/latex]<\/li>\n
    6. [latex]\\text{LCD}=3(4)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 4(x&+&1)&=&3(x&+&3) \\\\ 4x&+&4&=&3x&+&9 \\\\ -3x&-&4&&-3x&-&4 \\\\ \\hline &&x&=&5&& \\end{array}[\/latex]<\/li>\n
    7. [latex]\\text{LCD}=3(p+4)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrcrr} 2(3)&=&(p&+&4)(p&+&5) \\\\ 6&=&p^2&+&9p&+&20 \\\\ -6&&&&&-&6 \\\\ \\hline 0&=&p^2&+&9p&+&14 \\\\ 0&=&(p&+&7)(p&+&2) \\\\ \\\\ p&=&-2,&-7&&& \\\\ \\end{array}[\/latex]<\/li>\n
    8. [latex]\\text{LCD}=10(n+1)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrcrr} 5(10)&=&(n&-&4)(n&+&1) \\\\ 50&=&n^2&-&3n&-&4 \\\\ -50&&&&&-&50 \\\\ \\hline 0&=&n^2&-&3n&-&54 \\\\ 0&=&(n&-&9)(n&+&6) \\\\ \\\\ n&=&9,&-6&&& \\end{array}[\/latex]<\/li>\n
    9. [latex]\\text{LCD}=5(x-2)[\/latex]
      \n[latex]\\begin{array}[t]{rrcrrrl} (x&+&5)(x&-&2)&=&5(6) \\\\ x^2&+&3x&-&10&=&\\phantom{-}30 \\\\ &&&-&30&&-30 \\\\ \\hline x^2&+&3x&-&40&=&0 \\\\ (x&-&5)(x&+&8)&=&0 \\\\ \\\\ &&&&x&=&5, -7 \\end{array}[\/latex]<\/li>\n
    10. [latex]\\text{LCD}=5(x-3)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrcrr} 20&=&(x&-&3)(x&+&5) \\\\ 20&=&x^2&+&2x&-&15 \\\\ -20&&&&&-&20 \\\\ \\hline 0&=&x^2&+&2x&-&35 \\\\ 0&=&(x&-&5)(x&+&7) \\\\ \\\\ x&=&5,&-7&&& \\end{array}[\/latex]<\/li>\n
    11. [latex]\\text{LCD}=4(m-4)[\/latex]
      \n[latex]\\begin{array}[t]{rrcrrrl} (m&+&3)(m&-&4)&=&4(11) \\\\ m^2&-&m&-&12&=&\\phantom{-}44 \\\\ &&&-&44&&-44 \\\\ \\hline (m^2&-&m&-&56)&=&0 \\\\ (m&-&8)(m&+&7)&=&0 \\\\ \\\\ &&&&m&=&8, -7 \\end{array}[\/latex]<\/li>\n
    12. [latex]\\text{LCD}=8(x-1)[\/latex]
      \n[latex]\\begin{array}[t]{rrcrrrl} (x&-&5)(x&-&1)&=&4(8) \\\\ x^2&-&6x&+&5&=&\\phantom{-}32 \\\\ &&&-&32&&-32 \\\\ \\hline x^2&-&6x&-&27&=&0 \\\\ (x&-&9)(x&+&3)&=&0 \\\\ \\\\ &&&&x&=&9, -3 \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":79,"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-1948","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\/1948","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\/1948\/revisions"}],"predecessor-version":[{"id":1949,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1948\/revisions\/1949"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1948\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1948"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1948"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1948"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1948"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}