{"id":1976,"date":"2021-12-02T19:40:17","date_gmt":"2021-12-03T00:40:17","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-10-1\/"},"modified":"2022-11-02T10:38:51","modified_gmt":"2022-11-02T14:38:51","slug":"answer-key-10-1","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-10-1\/","title":{"raw":"Answer Key 10.1","rendered":"Answer Key 10.1"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n\\sqrt{2x+3}&-&3&=&0 \\\\\n&+&3&&+3 \\\\\n\\hline\n(\\sqrt{2x+3})^2&&&=&\\phantom{+}(3)^2 \\\\ \\\\\n2x&+&3&=&9 \\\\\n&-&3&&-3 \\\\\n\\hline\n&&\\dfrac{2x}{2}&=&\\dfrac{6}{2} \\\\ \\\\\n&&x&=&3\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n\\sqrt{5x+1}&-&4&=&0 \\\\\n&+&4&=&+4 \\\\\n\\hline\n(\\sqrt{5x+1})^2&&&=&(4)^2 \\\\ \\\\\n5x&+&1&=&16 \\\\\n&-&1&&-1 \\\\\n\\hline\n&&\\dfrac{5x}{5}&=&\\dfrac{15}{5} \\\\ \\\\\n&&x&=&3\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n\\sqrt{6x-5}&-&x&=&0&&&& \\\\\n&+&x&&+x&&&& \\\\\n\\hline\n(\\sqrt{6x-5})^2&&&=&(x)^2&&&& \\\\ \\\\\n6x&-&5&=&x^2&&&& \\\\\n-6x&+&5&&&-&6x&+&5 \\\\\n\\hline\n&&0&=&x^2&-&6x&+&5 \\\\\n&&0&=&(x&-&5)(x&-&1) \\\\ \\\\\n&&x&=&5,&1&&&\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex](\\sqrt{7x+8})^2=(x)^2[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}7x&+&8&=&x^2&&&& \\\\\n-7x&-&8&&&-&7x&-&8 \\\\\n\\hline\n&&0&=&x^2&-&7x&-&8 \\\\\n&&0&=&(x&-&8)(x&+&1) \\\\ \\\\\n&&x&=&-1,&8&&&\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex](\\sqrt{3+x})^2=(\\sqrt{6x+13})^2[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n3&+&x&=&6x&+&13 \\\\\n-3&-&6x&&-6x&-&3 \\\\\n\\hline\n&&\\dfrac{-5x}{-5}&=&\\dfrac{10}{-5}&& \\\\ \\\\\n&&x&=&-2&&\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex](\\sqrt{x-1})^2=(\\sqrt{7-x})^2[\/latex]\n[latex]\\begin{array}{rrrrrrr}\nx&-&1&=&7&-&x \\\\\n+x&+&1&&+1&+&x \\\\\n\\hline\n&&\\dfrac{2x}{2}&=&\\dfrac{8}{2}&& \\\\ \\\\\n&&x&=&4&&\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex](\\sqrt[3]{3-3x})^3=(\\sqrt[3]{2x-5})^3[\/latex]\n[latex]\\begin{array}{rrrrrrr}\n3&-&3x&=&2x&-&5 \\\\\n-3&-&2x&&-2x&-&3 \\\\\n\\hline\n&&\\dfrac{-5x}{-5}&=&\\dfrac{-8}{-5}&& \\\\ \\\\\n&&x&=&\\dfrac{8}{5}&&\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex](\\sqrt[4]{3x-2})^4=(\\sqrt[4]{x+4})^4[\/latex]\n[latex] \\begin{array}{rrrrrrr}\n3x&-&2&=&x&+&4 \\\\\n-x&+&2&&-x&+&2 \\\\\n\\hline\n&&\\dfrac{2x}{2}&=&\\dfrac{6}{2}&& \\\\ \\\\\n&&x&=&3&&\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex](\\sqrt{x+7})^2\\ge (2)^2[\/latex]\n[latex]\\begin{array}{rrrrr}\nx&+&7&\\ge &4 \\\\\n&-&7&&-7 \\\\\n\\hline\n&&x&\\ge &-3\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex](\\sqrt{x-2})^2\\le (4)^2[\/latex]\n[latex]\\begin{array}{rrrrr}\nx&-&2&\\le &16 \\\\\n&+&2&&+2 \\\\\n\\hline\n&&x&\\le &18\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex](3)^2 < (\\sqrt{3x+6})^2 \\le (6)^2[\/latex]\n[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr}\n9&<&3x&+&6&\\le &36 \\\\\n-6&&&-&6&&-6 \\\\\n\\hline\n\\dfrac{3}{3}&<&&\\dfrac{3x}{3}&&\\le &\\dfrac{30}{3} \\\\\n1&<&&x&&\\le &10\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex](0)^2 < (\\sqrt{x+5})^2 < (5)^2[\/latex]\n[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr}\n0&<&x&+&5&<&25 \\\\\n-5&&&-&5&&-5 \\\\\n\\hline\n-5&<&&x&&<&20\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} \\sqrt{2x+3}&-&3&=&0 \\\\ &+&3&&+3 \\\\ \\hline (\\sqrt{2x+3})^2&&&=&\\phantom{+}(3)^2 \\\\ \\\\ 2x&+&3&=&9 \\\\ &-&3&&-3 \\\\ \\hline &&\\dfrac{2x}{2}&=&\\dfrac{6}{2} \\\\ \\\\ &&x&=&3 \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} \\sqrt{5x+1}&-&4&=&0 \\\\ &+&4&=&+4 \\\\ \\hline (\\sqrt{5x+1})^2&&&=&(4)^2 \\\\ \\\\ 5x&+&1&=&16 \\\\ &-&1&&-1 \\\\ \\hline &&\\dfrac{5x}{5}&=&\\dfrac{15}{5} \\\\ \\\\ &&x&=&3 \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} \\sqrt{6x-5}&-&x&=&0&&&& \\\\ &+&x&&+x&&&& \\\\ \\hline (\\sqrt{6x-5})^2&&&=&(x)^2&&&& \\\\ \\\\ 6x&-&5&=&x^2&&&& \\\\ -6x&+&5&&&-&6x&+&5 \\\\ \\hline &&0&=&x^2&-&6x&+&5 \\\\ &&0&=&(x&-&5)(x&-&1) \\\\ \\\\ &&x&=&5,&1&&& \\end{array}[\/latex]<\/li>\n
    4. [latex](\\sqrt{7x+8})^2=(x)^2[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr}7x&+&8&=&x^2&&&& \\\\ -7x&-&8&&&-&7x&-&8 \\\\ \\hline &&0&=&x^2&-&7x&-&8 \\\\ &&0&=&(x&-&8)(x&+&1) \\\\ \\\\ &&x&=&-1,&8&&& \\end{array}[\/latex]<\/li>\n
    5. [latex](\\sqrt{3+x})^2=(\\sqrt{6x+13})^2[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 3&+&x&=&6x&+&13 \\\\ -3&-&6x&&-6x&-&3 \\\\ \\hline &&\\dfrac{-5x}{-5}&=&\\dfrac{10}{-5}&& \\\\ \\\\ &&x&=&-2&& \\end{array}[\/latex]<\/li>\n
    6. [latex](\\sqrt{x-1})^2=(\\sqrt{7-x})^2[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} x&-&1&=&7&-&x \\\\ +x&+&1&&+1&+&x \\\\ \\hline &&\\dfrac{2x}{2}&=&\\dfrac{8}{2}&& \\\\ \\\\ &&x&=&4&& \\end{array}[\/latex]<\/li>\n
    7. [latex](\\sqrt[3]{3-3x})^3=(\\sqrt[3]{2x-5})^3[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} 3&-&3x&=&2x&-&5 \\\\ -3&-&2x&&-2x&-&3 \\\\ \\hline &&\\dfrac{-5x}{-5}&=&\\dfrac{-8}{-5}&& \\\\ \\\\ &&x&=&\\dfrac{8}{5}&& \\end{array}[\/latex]<\/li>\n
    8. [latex](\\sqrt[4]{3x-2})^4=(\\sqrt[4]{x+4})^4[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} 3x&-&2&=&x&+&4 \\\\ -x&+&2&&-x&+&2 \\\\ \\hline &&\\dfrac{2x}{2}&=&\\dfrac{6}{2}&& \\\\ \\\\ &&x&=&3&& \\end{array}[\/latex]<\/li>\n
    9. [latex](\\sqrt{x+7})^2\\ge (2)^2[\/latex]
      \n[latex]\\begin{array}{rrrrr} x&+&7&\\ge &4 \\\\ &-&7&&-7 \\\\ \\hline &&x&\\ge &-3 \\end{array}[\/latex]<\/li>\n
    10. [latex](\\sqrt{x-2})^2\\le (4)^2[\/latex]
      \n[latex]\\begin{array}{rrrrr} x&-&2&\\le &16 \\\\ &+&2&&+2 \\\\ \\hline &&x&\\le &18 \\end{array}[\/latex]<\/li>\n
    11. [latex](3)^2 < (\\sqrt{3x+6})^2 \\le (6)^2[\/latex]\n[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr} 9&<&3x&+&6&\\le &36 \\\\ -6&&&-&6&&-6 \\\\ \\hline \\dfrac{3}{3}&<&&\\dfrac{3x}{3}&&\\le &\\dfrac{30}{3} \\\\ 1&<&&x&&\\le &10 \\end{array}[\/latex]<\/li>\n
    12. [latex](0)^2 < (\\sqrt{x+5})^2 < (5)^2[\/latex]\n[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr} 0&<&x&+&5&<&25 \\\\ -5&&&-&5&&-5 \\\\ \\hline -5&<&&x&&<&20 \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":93,"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-1976","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\/1976","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\/1976\/revisions"}],"predecessor-version":[{"id":1977,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1976\/revisions\/1977"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1976\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1976"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1976"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1976"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}