{"id":5021,"date":"2016-07-20T21:07:59","date_gmt":"2016-07-20T21:07:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/microeconomics\/?post_type=chapter&p=5021"},"modified":"2016-08-02T16:35:25","modified_gmt":"2016-08-02T16:35:25","slug":"reading-solving-simple-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/atd-herkimer-microeconomics\/chapter\/reading-solving-simple-equations\/","title":{"raw":"Reading: Solving Simple Equations","rendered":"Reading: Solving Simple Equations"},"content":{"raw":"Let's quickly review some math concepts that will help you avoid simple errors in your work.\r\n

Order of Operations<\/h2>\r\nRemember, when you solve an equation it's important to do each operation in the following\u00a0order:\r\n
    \r\n \t
  1. Simplify inside parentheses and brackets.<\/li>\r\n \t
  2. Simplify the exponent.<\/li>\r\n \t
  3. Multiply and divide from left to right.<\/li>\r\n \t
  4. Add and subtract from left to right.<\/li>\r\n<\/ol>\r\nIn this course you will not use exponents, but you will need to remember the order of the other steps.\r\n\r\nSo, in solving the following equation, you multiply first, then add:\r\n

    [latex]\\begin{array}{l}y=9+3\\times10\\\\y=9+30\\\\y=39\\end{array}[\/latex]<\/p>\r\n\r\n

    Lines<\/h2>\r\nIn this course the most common equation you will see is [latex]y=b+mx[\/latex]. This is the equation for a line. We will revisit this equation later in this module when we review graphs. For now, let's practice solving this common equation using different variables.\r\n

    Understanding Variables<\/h2>\r\nTo a mathematician or an economist, a variable<\/span><\/strong> is the name given to a quantity that can\u00a0assume a range of values. In other words, the value of a variable can change or vary. In an equation it's represented by a letter or a symbol.\r\n\r\nBecause economic models often consider cause and effect, variables are important.\u00a0You will often be asked to consider a range of options that result from different variables. Below is a very simple example:\r\n

    [latex]y=9+3x[\/latex]<\/p>\r\nIn order to understand the range of options, we might start with 0. What does y<\/em> equal if [latex]x=0[\/latex]?\r\n

    [latex]\\begin{array}{l}y=9+3x\\\\y=9+3(0)\\\\y=9+0\\\\y=9\\end{array}[\/latex]<\/p>\r\nNow, let's look at the same formula with different information.\u00a0\u00a0What does y equal if [latex]x=5[\/latex]?\r\n

    [latex]\\begin{array}{l}y=9+3x\\\\y=9+3(5)\\\\y=9+15\\\\y=24\\end{array}[\/latex]<\/p>\r\n\r\n

    Working with Variables<\/strong><\/h2>\r\nRemember that when\u00a0you're trying to solve an equation with one or more variables, you\u00a0need\u00a0to isolate the variable. Let's walk through a simple example using the same equation from above.\r\n\r\nWhat if we want\u00a0to solve the equation in a case where [latex]y=24[\/latex]?\r\n

    [latex]\\begin{array}{r}y=9+3x\\\\24=9+3x\\end{array}[\/latex]<\/p>\r\n

    First, subtract the same number from each side of the equation to\u00a0simplify the equation without changing the fact that it's an equality. In this case, we want to subtract the number that will enable\u00a0us to isolate x<\/em> (x<\/em> is on one side of the equal sign all by itself). We can do that by subtracting 9 from each side.<\/p>\r\n

    [latex]\\begin{array}{l}\\,24=9+3x\\\\-9=-9\\\\\\,15=3x\\end{array}[\/latex]<\/p>\r\nNow we can further simplify the equation by dividing both sides by 3.\r\n

    [latex]\\begin{array}{l}\\underline{15}=\\underline{3x}\\\\\\,\\,3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\\\\\,\\,\\,5=x\\end{array}[\/latex]<\/p>\r\nLet's practice solving for x<\/em> one more time. What does x<\/em>\u00a0equal if [latex]y=12[\/latex]?\r\n

    [latex]\\,\\,12=9+3x\\\\-9=-9\\\\\\,\\,\\,\\,\\,3=3x\\\\\\,\\,\\,\\,\\,\\underline{3}=\\underline{3x}\\\\\\,\\,\\,\\,\\,3\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\\\\\,\\,\\,\\,\\,\\,1=x[\/latex]<\/p>\r\n\r\n

    Self Check:\u00a0Math in Economics<\/h2>\r\nAnswer the question(s) below to see how well you understand the topics covered in the previous section. This short quiz does not\u00a0<\/strong>count toward your grade in the class, and you can retake it an unlimited number of times.\r\n

    You\u2019ll have more success on the Self Check if you\u2019ve completed the two\u00a0Readings in this section.<\/span><\/p>\r\nUse this quiz to check your understanding and decide whether to (1) study the previous section further or (2) move on to the next section.\r\n\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/1547","rendered":"

    Let’s quickly review some math concepts that will help you avoid simple errors in your work.<\/p>\n

    Order of Operations<\/h2>\n

    Remember, when you solve an equation it’s important to do each operation in the following\u00a0order:<\/p>\n

      \n
    1. Simplify inside parentheses and brackets.<\/li>\n
    2. Simplify the exponent.<\/li>\n
    3. Multiply and divide from left to right.<\/li>\n
    4. Add and subtract from left to right.<\/li>\n<\/ol>\n

      In this course you will not use exponents, but you will need to remember the order of the other steps.<\/p>\n

      So, in solving the following equation, you multiply first, then add:<\/p>\n

      [latex]\\begin{array}{l}y=9+3\\times10\\\\y=9+30\\\\y=39\\end{array}[\/latex]<\/p>\n

      Lines<\/h2>\n

      In this course the most common equation you will see is [latex]y=b+mx[\/latex]. This is the equation for a line. We will revisit this equation later in this module when we review graphs. For now, let’s practice solving this common equation using different variables.<\/p>\n

      Understanding Variables<\/h2>\n

      To a mathematician or an economist, a variable<\/span><\/strong> is the name given to a quantity that can\u00a0assume a range of values. In other words, the value of a variable can change or vary. In an equation it’s represented by a letter or a symbol.<\/p>\n

      Because economic models often consider cause and effect, variables are important.\u00a0You will often be asked to consider a range of options that result from different variables. Below is a very simple example:<\/p>\n

      [latex]y=9+3x[\/latex]<\/p>\n

      In order to understand the range of options, we might start with 0. What does y<\/em> equal if [latex]x=0[\/latex]?<\/p>\n

      [latex]\\begin{array}{l}y=9+3x\\\\y=9+3(0)\\\\y=9+0\\\\y=9\\end{array}[\/latex]<\/p>\n

      Now, let’s look at the same formula with different information.\u00a0\u00a0What does y equal if [latex]x=5[\/latex]?<\/p>\n

      [latex]\\begin{array}{l}y=9+3x\\\\y=9+3(5)\\\\y=9+15\\\\y=24\\end{array}[\/latex]<\/p>\n

      Working with Variables<\/strong><\/h2>\n

      Remember that when\u00a0you’re trying to solve an equation with one or more variables, you\u00a0need\u00a0to isolate the variable. Let’s walk through a simple example using the same equation from above.<\/p>\n

      What if we want\u00a0to solve the equation in a case where [latex]y=24[\/latex]?<\/p>\n

      [latex]\\begin{array}{r}y=9+3x\\\\24=9+3x\\end{array}[\/latex]<\/p>\n

      First, subtract the same number from each side of the equation to\u00a0simplify the equation without changing the fact that it’s an equality. In this case, we want to subtract the number that will enable\u00a0us to isolate x<\/em> (x<\/em> is on one side of the equal sign all by itself). We can do that by subtracting 9 from each side.<\/p>\n

      [latex]\\begin{array}{l}\\,24=9+3x\\\\-9=-9\\\\\\,15=3x\\end{array}[\/latex]<\/p>\n

      Now we can further simplify the equation by dividing both sides by 3.<\/p>\n

      [latex]\\begin{array}{l}\\underline{15}=\\underline{3x}\\\\\\,\\,3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\\\\\,\\,\\,5=x\\end{array}[\/latex]<\/p>\n

      Let’s practice solving for x<\/em> one more time. What does x<\/em>\u00a0equal if [latex]y=12[\/latex]?<\/p>\n

      [latex]\\,\\,12=9+3x\\\\-9=-9\\\\\\,\\,\\,\\,\\,3=3x\\\\\\,\\,\\,\\,\\,\\underline{3}=\\underline{3x}\\\\\\,\\,\\,\\,\\,3\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\\\\\,\\,\\,\\,\\,\\,1=x[\/latex]<\/p>\n

      Self Check:\u00a0Math in Economics<\/h2>\n

      Answer the question(s) below to see how well you understand the topics covered in the previous section. This short quiz does not\u00a0<\/strong>count toward your grade in the class, and you can retake it an unlimited number of times.<\/p>\n

      You\u2019ll have more success on the Self Check if you\u2019ve completed the two\u00a0Readings in this section.<\/span><\/p>\n

      Use this quiz to check your understanding and decide whether to (1) study the previous section further or (2) move on to the next section.<\/p>\n

      \t