{"id":412,"date":"2019-04-29T12:52:25","date_gmt":"2019-04-29T16:52:25","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=chapter&p=412"},"modified":"2019-11-21T16:32:59","modified_gmt":"2019-11-21T21:32:59","slug":"2-2-solving-linear-equations","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/chapter\/2-2-solving-linear-equations\/","title":{"raw":"2.2 Solving Linear Equations","rendered":"2.2 Solving Linear Equations"},"content":{"raw":"[latexpage]\r\n\r\nWhen working with questions that require two or more steps to solve, do the reverse of the order of operations to solve for the variable.\r\n
\r\n

Example 2.2.1<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nSolve \\(4x+16=-4\\) for \\(x.\\)\r\n

\\(\\begin{array}{rrrrrl}\r\n4x& +& 16 &=&-4& \\\\\r\n&&-16&& -16&\\text{Subtract 16 from each side}\u00a0\\\\\r\n\\midrule\r\n&&\\dfrac{4x}{4}& =& \\dfrac{-20}{4}&\\text{Divide each side by 4}\\\\ \\\\\r\n&&x& =& -5 & \\text{Solution}\r\n\\end{array}\\)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nIn solving the above equation, notice that the general pattern followed was to do the opposite of the equation. \\(4x\\) was added to 16, so 16 was then subtracted from both sides. The variable \\(x\\) was multiplied by 4, so both sides were divided by 4.\r\n

\r\n

Example 2.2.2<\/p>\r\n\r\n<\/header>\r\n

\r\n
    \r\n \t
  1. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n5x &+& 7 &=& 7 \\\\\r\n&-&7&&-7 \\\\\r\n\\midrule\r\n&&\\dfrac{5x}{5} &=& \\dfrac{0}{5}\\\\ \\\\\r\n&&x& =& 0\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n4 &- &2x& =& 10 \\\\\r\n-4&&&&-4\\\\\r\n\\midrule\r\n&&\\dfrac{-2x}{-2}& = &\\dfrac{6}{-2}\\\\ \\\\\r\n&&x& =& -3\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-3x& -& 7& =& 8 \\\\\r\n&+&7& = & + 7 \\\\\r\n\\midrule\r\n&&\\dfrac{-3x}{-3}& =& \\dfrac{15}{-3} \\\\ \\\\\r\n&&x &= &-5\\\\\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n\r\n<\/div>\r\n

    Questions<\/h1>\r\nFor questions 1 to 20, solve each linear equation.\r\n
      \r\n \t
    1. \\(5 + \\dfrac{n}{4} = 4\\)<\/li>\r\n \t
    2. \\(-2 = -2m + 12\\)<\/li>\r\n \t
    3. \\(102 = -7r + 4\\)<\/li>\r\n \t
    4. \\(27 = 21 - 3x\\)<\/li>\r\n \t
    5. \\(-8n + 3 = -77\\)<\/li>\r\n \t
    6. \\(-4 - b = 8\\)<\/li>\r\n \t
    7. \\(0 = -6v\\)<\/li>\r\n \t
    8. \\(-2 + \\dfrac{x}{2} = 4\\)<\/li>\r\n \t
    9. \\(-8 = \\dfrac{x}{5} - 6\\)<\/li>\r\n \t
    10. \\(-5 = \\dfrac{a}{4} - 1\\)<\/li>\r\n \t
    11. \u00a0\\(0 = -7 + \\dfrac{k}{2}\\)<\/li>\r\n \t
    12. \\(-6 = 15 + 3p\\)<\/li>\r\n \t
    13. \\(-12 + 3x = 0\\)<\/li>\r\n \t
    14. \\(-5m + 2 = 27\\)<\/li>\r\n \t
    15. \\(\\dfrac{b}{3} + 7 = 10\\)<\/li>\r\n \t
    16. \\(\\dfrac{x}{1} - 8 = -8\\)<\/li>\r\n \t
    17. \\(152 = 8n + 64\\)<\/li>\r\n \t
    18. \\(-11 = -8 + \\dfrac{v}{2}\\)<\/li>\r\n \t
    19. \\(-16 = 8a + 64\\)<\/li>\r\n \t
    20. \\(-2x - 3 = -29\\)<\/li>\r\n<\/ol>\r\nAnswer Key 2.2<\/a>","rendered":"

      When working with questions that require two or more steps to solve, do the reverse of the order of operations to solve for the variable.<\/p>\n

      \n
      \n

      Example 2.2.1<\/p>\n<\/header>\n

      \n

      Solve \"4x+16=-4\" for \"x.\"<\/p>\n

      \"\begin{array}{rrrrrl}<\/p>\n<\/div>\n<\/div>\n

      In solving the above equation, notice that the general pattern followed was to do the opposite of the equation. \"4x\" was added to 16, so 16 was then subtracted from both sides. The variable \"x\" was multiplied by 4, so both sides were divided by 4.<\/p>\n

      \n
      \n

      Example 2.2.2<\/p>\n<\/header>\n

      \n
        \n
      1. \"\begin{array}{rrrrr}<\/li>\n
      2. \"\begin{array}{rrrrr}<\/li>\n
      3. \"\begin{array}{rrrrr}<\/li>\n<\/ol>\n<\/div>\n

         <\/p>\n<\/div>\n

        Questions<\/h1>\n

        For questions 1 to 20, solve each linear equation.<\/p>\n

          \n
        1. \"5 + \dfrac{n}{4} = 4\"<\/li>\n
        2. \"-2 = -2m + 12\"<\/li>\n
        3. \"102 = -7r + 4\"<\/li>\n
        4. \"27 = 21 - 3x\"<\/li>\n
        5. \"-8n + 3 = -77\"<\/li>\n
        6. \"-4 - b = 8\"<\/li>\n
        7. \"0 = -6v\"<\/li>\n
        8. \"-2 + \dfrac{x}{2} = 4\"<\/li>\n
        9. \"-8 = \dfrac{x}{5} - 6\"<\/li>\n
        10. \"-5 = \dfrac{a}{4} - 1\"<\/li>\n
        11. \u00a0\"0 = -7 + \dfrac{k}{2}\"<\/li>\n
        12. \"-6 = 15 + 3p\"<\/li>\n
        13. \"-12 + 3x = 0\"<\/li>\n
        14. \"-5m + 2 = 27\"<\/li>\n
        15. \"\dfrac{b}{3} + 7 = 10\"<\/li>\n
        16. \"\dfrac{x}{1} - 8 = -8\"<\/li>\n
        17. \"152 = 8n + 64\"<\/li>\n
        18. \"-11 = -8 + \dfrac{v}{2}\"<\/li>\n
        19. \"-16 = 8a + 64\"<\/li>\n
        20. \"-2x - 3 = -29\"<\/li>\n<\/ol>\n

          Answer Key 2.2<\/a><\/p>\n","protected":false},"author":14,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-412","chapter","type-chapter","status-publish","hentry"],"part":358,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters\/412","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters\/412\/revisions"}],"predecessor-version":[{"id":3424,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters\/412\/revisions\/3424"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/parts\/358"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters\/412\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=412"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapter-type?post=412"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=412"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}