{"id":6632,"date":"2017-05-02T20:10:04","date_gmt":"2017-05-02T20:10:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=6632"},"modified":"2019-05-24T18:02:55","modified_gmt":"2019-05-24T18:02:55","slug":"solve-equations-using-integers-the-division-property-of-equality","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/solve-equations-using-integers-the-division-property-of-equality\/","title":{"raw":"Introduction to Solving One-step Equations Using Integers","rendered":"Introduction to Solving One-step Equations Using Integers"},"content":{"raw":"

What you'll learn to do: Solve one-step equations using integers<\/h2>\r\n[caption id=\"attachment_12953\" align=\"aligncenter\" width=\"744\"]\"A<\/a> The apples are picked--now it's time to divvy them up![\/caption]\r\n\r\nAfter a day of apple picking, Jessica, Mark, and Kim decide to split up their apples equally. In their shared basket, they count [latex]39[\/latex] apples total. How many apples can each of them take home? To find out, they'll need to use division in a one-step variable equation. In this section, you'll learn\u00a0how to maintain equality on both sides of the equation and solve for a variable.\r\n\r\nBefore you get started, take this readiness quiz.\r\n
\r\n

readiness quiz<\/h3>\r\n1)\r\n\r\n[ohm_question]144878[\/ohm_question]\r\n\r\nIf you missed this problem, review this example.\r\n
\r\n\r\nEvaluate [latex]x+7[\/latex] when\r\n
    \r\n \t
  1. [latex]x=3[\/latex]<\/li>\r\n \t
  2. [latex]x=12[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"998927\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"998927\"]\r\n\r\nSolution:\r\n\r\n1. To evaluate, substitute [latex]3[\/latex] for [latex]x[\/latex] in the expression, and then simplify.\r\n\r\n\r\n\r\n\r\n\r\n
    <\/td>\r\n[latex]x+7[\/latex]<\/td>\r\n<\/tr>\r\n
    Substitute.<\/td>\r\n[latex]\\color{red}{3}+7[\/latex]<\/td>\r\n<\/tr>\r\n
    Add.<\/td>\r\n[latex]10[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=3[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]10[\/latex].\r\n2. To evaluate, substitute [latex]12[\/latex] for [latex]x[\/latex] in the expression, and then simplify.\r\n\r\n\r\n\r\n\r\n\r\n
    <\/td>\r\n[latex]x+7[\/latex]<\/td>\r\n<\/tr>\r\n
    Substitute.<\/td>\r\n[latex]\\color{red}{12}+7[\/latex]<\/td>\r\n<\/tr>\r\n
    Add.<\/td>\r\n[latex]19[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=12[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]19[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n2)\r\n\r\n[ohm_question]141843[\/ohm_question]\r\n\r\nIf you missed this problem, review the example below.\r\n
    \r\n\r\nEvaluate [latex]9x - 2,[\/latex] when\r\n
      \r\n \t
    1. [latex]x=5[\/latex]<\/li>\r\n \t
    2. [latex]x=1[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"711463\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"711463\"]\r\n\r\nSolution\r\nRemember [latex]ab[\/latex] means [latex]a[\/latex] times [latex]b[\/latex], so [latex]9x[\/latex] means [latex]9[\/latex] times [latex]x[\/latex].\r\n1. To evaluate the expression when [latex]x=5[\/latex], we substitute [latex]5[\/latex] for [latex]x[\/latex], and then simplify.\r\n\r\n\r\n\r\n\r\n\r\n\r\n
      <\/td>\r\n[latex]9x-2[\/latex]<\/td>\r\n<\/tr>\r\n
      Substitute [latex]\\color{red}{5}[\/latex] for x.<\/td>\r\n[latex]9\\cdot\\color{red}{5}-2[\/latex]<\/td>\r\n<\/tr>\r\n
      Multiply.<\/td>\r\n[latex]45-2[\/latex]<\/td>\r\n<\/tr>\r\n
      Subtract.<\/td>\r\n[latex]43[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. To evaluate the expression when [latex]x=1[\/latex], we substitute [latex]1[\/latex] for [latex]x[\/latex], and then simplify.\r\n\r\n\r\n\r\n\r\n\r\n\r\n
      <\/td>\r\n[latex]9x-2[\/latex]<\/td>\r\n<\/tr>\r\n
      Substitute [latex]\\color{red}{1}[\/latex] for x.<\/td>\r\n[latex]9(\\color{red}{1})-2[\/latex]<\/td>\r\n<\/tr>\r\n
      Multiply.<\/td>\r\n[latex]9-2[\/latex]<\/td>\r\n<\/tr>\r\n
      Subtract.<\/td>\r\n[latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that in part 1 that we wrote [latex]9\\cdot 5[\/latex] and in part 2 we wrote [latex]9\\left(1\\right)[\/latex]. Both the dot and the parentheses tell us to multiply.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n3)\r\n\r\n[ohm_question]144907[\/ohm_question]\r\n\r\nIf you missed this problem, review the following video\r\n\r\nhttps:\/\/www.youtube.com\/watch?v=Hub7ku7UHT4&feature=youtu.be\r\n\r\n<\/div>","rendered":"

      What you’ll learn to do: Solve one-step equations using integers<\/h2>\n
      \"A<\/a><\/p>\n

      The apples are picked–now it’s time to divvy them up!<\/p>\n<\/div>\n

      After a day of apple picking, Jessica, Mark, and Kim decide to split up their apples equally. In their shared basket, they count [latex]39[\/latex] apples total. How many apples can each of them take home? To find out, they’ll need to use division in a one-step variable equation. In this section, you’ll learn\u00a0how to maintain equality on both sides of the equation and solve for a variable.<\/p>\n

      Before you get started, take this readiness quiz.<\/p>\n

      \n

      readiness quiz<\/h3>\n

      1)<\/p>\n