{"id":1654,"date":"2021-12-02T19:38:56","date_gmt":"2021-12-03T00:38:56","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-7\/"},"modified":"2022-11-02T10:37:08","modified_gmt":"2022-11-02T14:37:08","slug":"answer-key-3-7","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-3-7\/","title":{"raw":"Answer Key 3.7","rendered":"Answer Key 3.7"},"content":{"raw":"
    \n \t
  1. [latex]2x+5=25[\/latex]<\/li>\n \t
  2. [latex]4x+12=36[\/latex]<\/li>\n \t
  3. [latex]3x-8=22[\/latex]<\/li>\n \t
  4. [latex]6x-8=22[\/latex]<\/li>\n \t
  5. [latex]x-8=\\dfrac{x}{2}[\/latex]<\/li>\n \t
  6. [latex]x-4=\\dfrac{x}{2}[\/latex]<\/li>\n \t
  7. [latex]x+x+1+x+2=21[\/latex]<\/li>\n \t
  8. [latex]x+x+2-(x+4)=5[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n5&+&3x&=&17& \\\\\n-5&&&&-5& \\\\\n\\hline\n&&3x&=&12& \\\\ \\\\\n&&x&=&\\dfrac{12}{3}&\\text{or } 4\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n3x&-&5&=&10& \\\\\n&+&5&&+5& \\\\\n\\hline\n&&3x&=&15& \\\\ \\\\\n&&x&=&\\dfrac{15}{3}&\\text{or } 5\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n60&+&9x&=&10x&-&2 \\\\\n+2&-&9x&&-9x&+&2 \\\\\n\\hline\n&&62&=&x&&\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n7x&-&11&=&6x&+&5 \\\\\n-6x&+&11&&-6x&+&11 \\\\\n\\hline\n&&x&=&16&&\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrl}\nx&+&x&+&1&+&x&+&2&=&108 \\\\\n&&&&&&3x&+&3&=&108 \\\\\n&&&&&&&-&3&&-3 \\\\\n\\hline\n&&&&&&&&3x&=&105 \\\\ \\\\\n&&&&&&&&x&=&\\dfrac{105}{3}\\text{ or }35 \\\\ \\\\\n&&&&&&&&&\\therefore &35, 36, 37\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrl}\nx&+&x&+&1&+&x&+&2&=&-126 \\\\\n&&&&&&3x&+&3&=&-126 \\\\\n&&&&&&&-&3&&-\\phantom{00}3 \\\\\n\\hline\n&&&&&&&&3x&=&-129 \\\\ \\\\\n&&&&&&&&x&=&\\dfrac{-129}{3}\\text{ or }-43 \\\\ \\\\\n&&&&&&&&&\\therefore &-43, -42, -41\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrl}\nx&+&2(x&+&1)&+&3(x&+&2)&=&-76 \\\\\nx&+&2x&+&2&+&3x&+&6&=&-76 \\\\\n&&&&&&6x&+&8&=&-76 \\\\\n&&&&&&&-&8&&-\\phantom{0}8 \\\\\n\\hline\n&&&&&&&&6x&=&-84 \\\\ \\\\\n&&&&&&&&x&=&\\dfrac{-84}{6}\\text{ or }-14 \\\\ \\\\\n&&&&&&&&&\\therefore &-14, -13, -12\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrl}\nx&+&2(x&+&2)&+&3(x&+&4)&=&\\phantom{0}70 \\\\\nx&+&2x&+&4&+&3x&+&12&=&\\phantom{0}70 \\\\\n&&&&&&6x&+&16&=&\\phantom{0}70 \\\\\n&&&&&&&-&16&&-16 \\\\\n\\hline\n&&&&&&&&6x&=&54 \\\\ \\\\\n&&&&&&&&x&=&\\dfrac{54}{6}\\text{ or }9 \\\\ \\\\\n&&&&&&&&&\\therefore &9,11,13\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]2x+5=25[\/latex]<\/li>\n
    2. [latex]4x+12=36[\/latex]<\/li>\n
    3. [latex]3x-8=22[\/latex]<\/li>\n
    4. [latex]6x-8=22[\/latex]<\/li>\n
    5. [latex]x-8=\\dfrac{x}{2}[\/latex]<\/li>\n
    6. [latex]x-4=\\dfrac{x}{2}[\/latex]<\/li>\n
    7. [latex]x+x+1+x+2=21[\/latex]<\/li>\n
    8. [latex]x+x+2-(x+4)=5[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} 5&+&3x&=&17& \\\\ -5&&&&-5& \\\\ \\hline &&3x&=&12& \\\\ \\\\ &&x&=&\\dfrac{12}{3}&\\text{or } 4 \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} 3x&-&5&=&10& \\\\ &+&5&&+5& \\\\ \\hline &&3x&=&15& \\\\ \\\\ &&x&=&\\dfrac{15}{3}&\\text{or } 5 \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 60&+&9x&=&10x&-&2 \\\\ +2&-&9x&&-9x&+&2 \\\\ \\hline &&62&=&x&& \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 7x&-&11&=&6x&+&5 \\\\ -6x&+&11&&-6x&+&11 \\\\ \\hline &&x&=&16&& \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrl} x&+&x&+&1&+&x&+&2&=&108 \\\\ &&&&&&3x&+&3&=&108 \\\\ &&&&&&&-&3&&-3 \\\\ \\hline &&&&&&&&3x&=&105 \\\\ \\\\ &&&&&&&&x&=&\\dfrac{105}{3}\\text{ or }35 \\\\ \\\\ &&&&&&&&&\\therefore &35, 36, 37 \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrl} x&+&x&+&1&+&x&+&2&=&-126 \\\\ &&&&&&3x&+&3&=&-126 \\\\ &&&&&&&-&3&&-\\phantom{00}3 \\\\ \\hline &&&&&&&&3x&=&-129 \\\\ \\\\ &&&&&&&&x&=&\\dfrac{-129}{3}\\text{ or }-43 \\\\ \\\\ &&&&&&&&&\\therefore &-43, -42, -41 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrl} x&+&2(x&+&1)&+&3(x&+&2)&=&-76 \\\\ x&+&2x&+&2&+&3x&+&6&=&-76 \\\\ &&&&&&6x&+&8&=&-76 \\\\ &&&&&&&-&8&&-\\phantom{0}8 \\\\ \\hline &&&&&&&&6x&=&-84 \\\\ \\\\ &&&&&&&&x&=&\\dfrac{-84}{6}\\text{ or }-14 \\\\ \\\\ &&&&&&&&&\\therefore &-14, -13, -12 \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrl} x&+&2(x&+&2)&+&3(x&+&4)&=&\\phantom{0}70 \\\\ x&+&2x&+&4&+&3x&+&12&=&\\phantom{0}70 \\\\ &&&&&&6x&+&16&=&\\phantom{0}70 \\\\ &&&&&&&-&16&&-16 \\\\ \\hline &&&&&&&&6x&=&54 \\\\ \\\\ &&&&&&&&x&=&\\dfrac{54}{6}\\text{ or }9 \\\\ \\\\ &&&&&&&&&\\therefore &9,11,13 \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":29,"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-1654","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\/1654","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\/1654\/revisions"}],"predecessor-version":[{"id":1655,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1654\/revisions\/1655"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1654\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1654"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1654"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1654"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}