Solving equations

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Solving equations

  1. 1. Solving 1 and 2 step Equations Algebra 1 Jon Wells
  2. 2. Keep the equation balanced <ul><li>Think of an equation like a balance scale where the equal sign is the pivot of the scale. Each side of the equal sign are expressions that are the same value (weight). You must simplify the expressions by taking the same amount of “weight” from each side. </li></ul>
  3. 3. Use inverse operations <ul><li>Use inverse (opposite) operations to simplify each side so that you get the variable by itself. For example, use subtraction to cancel addition. </li></ul><ul><li>Click this link to see a narrated video example </li></ul><ul><li>Example #1 </li></ul><ul><li>X+4 = 9 </li></ul><ul><li>-4 -4 </li></ul><ul><li>X = 5 </li></ul><ul><li>Example #2 </li></ul><ul><li>X+14 = 42 </li></ul><ul><li>-14 -14 </li></ul><ul><li>X = 28 </li></ul>
  4. 4. More examples <ul><li>Use addition to cancel subtraction </li></ul><ul><li>P-24 = 39 </li></ul><ul><li>+24 +24 </li></ul><ul><li>P = 63 </li></ul><ul><li>Use multiplication to cancel division </li></ul><ul><li>Q/13=7 </li></ul><ul><li>x13 x13 </li></ul><ul><li>Q = 91 </li></ul><ul><li>Use division to cancel multiplication </li></ul><ul><li>6r=54 </li></ul><ul><li>/6 /6 </li></ul><ul><li>r = 9 </li></ul><ul><li>*Multiply by the reciprocal to cancel fractions that are multiplied to variables </li></ul><ul><li>¾T = 12 </li></ul><ul><li>(4/3) ¾T = 12 (4/3) </li></ul><ul><li>T = 16 </li></ul>
  5. 5. Multiple step equations <ul><li>When equations have multiple terms on either side it takes more steps. </li></ul><ul><li>Solve 3x + 5 = 49 – x Steps: </li></ul><ul><li> + x + x 1. Get variables to one side </li></ul><ul><li> 4x + 5 = 49 </li></ul><ul><li> -5 -5 2. Get numbers to the other side </li></ul><ul><li> 4x = 44 </li></ul><ul><li> /4 /4 3. Get the variable by itself </li></ul><ul><li> x = 11 </li></ul><ul><li>3(11) + 5 = 49 – 11 4. Check you answer with substitution </li></ul><ul><li> 38 = 38 </li></ul>
  6. 6. Practice <ul><li>Click for example video </li></ul><ul><li>Click this link and use the balance scale and solve at least 10 problems. </li></ul>
  7. 7. Needs Assessment <ul><li>What do you know? </li></ul><ul><li>Variables are placeholders for unknown values. </li></ul><ul><li>To solve an equation means to figure out what the variable is equal to. </li></ul><ul><li>What do you want to know? </li></ul><ul><li>How to solve equations with addition, subtraction, multiplication, and division. </li></ul><ul><li>What are you trying to measure, determine, or define? </li></ul><ul><ul><ul><li>A process to solve equations </li></ul></ul></ul><ul><li>How will you collect and record information. </li></ul><ul><ul><ul><li>Notes in a notebook </li></ul></ul></ul><ul><li>Are all interested groups included in planning and conducting the needs assessment? </li></ul><ul><li>Only the teacher is involved in planning the needs assessment. </li></ul>
  8. 8. Sources <ul><li>Utah State University. (1999-2010). National library of virtual manipulatives . Retrieved from http://nlvm.usu.edu/ </li></ul>

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