Solving One Step Equations

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Beginning Algebra

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Solving One Step Equations

  1. 1. Solving one step equations Notes 3-2 & 3-3
  2. 2. Properties of Equality <ul><li>Addition : If a = b then a + c = b + c . </li></ul><ul><li>2. Subtraction : If a = b then a – c = b– c . </li></ul><ul><li>3. Multiplication : If a = b then ac = b c. </li></ul><ul><li>4. Division : If a = b and c ≠ 0 then a / c = b / c </li></ul>
  3. 3. Rules to Remember <ul><li>Quick Facts and Definitions: </li></ul><ul><li>When solving an equation, the goal is to get the variable by itself on one side of the equation. </li></ul><ul><li>Addition and subtraction are inverse operations. (opposites) </li></ul><ul><li>Multiplication and division are inverse operations. (opposites) </li></ul>
  4. 4. Solving Equations Requires BALANCE! <ul><li>Your equals sign will be the fulcrum (balancing point)! </li></ul><ul><li>Just remember, whatever you do to one side must be done to the other side to maintain balance…….. </li></ul>
  5. 5. Addition / Subtraction <ul><li>If the number to move is positive, subtract it from both sides of the equation. </li></ul><ul><li>If the number to move is negative, add its positive value to both sides of the equation. </li></ul>
  6. 6. Solving with Addition <ul><li>Solve the following equation for x: </li></ul><ul><li>x – 4 = 9 </li></ul><ul><li> + 4 +4 </li></ul><ul><li> x = 13 </li></ul><ul><li>We are able to get the x by itself </li></ul><ul><li>by ADDING 4 to each side! </li></ul><ul><li>(you WILL show this step in your homework!!) </li></ul>
  7. 7. Solving with Subtraction <ul><li>Solve the following equation for p: </li></ul><ul><li>p + 7 = 21 </li></ul><ul><li> - 7 - 7 </li></ul><ul><li>p = 14 </li></ul><ul><li>We are able to get the p by itself </li></ul><ul><li>by SUBTRACTING 7 from each side! </li></ul><ul><li>(you WILL show this step in your homework!!) </li></ul>
  8. 8. Solving with Division <ul><li>Solve the following equation for m: </li></ul><ul><li> 3 m = 18 </li></ul><ul><li>Divide both sides by 3 and simplify -- your work should look like this : </li></ul><ul><li>3 m = 18 </li></ul><ul><li>3 3 </li></ul><ul><li>m = 6 </li></ul><ul><li>(you WILL show this step in your homework!!) </li></ul>
  9. 9. Solving with Multiplication <ul><li>Problems involving fractions are solved using multiplication, and the knowledge of multiplicative inverses (reciprocals) </li></ul>
  10. 10. Example : <ul><li>Solve the following equation for n: </li></ul><ul><li>2n = 3 </li></ul><ul><li> 5 7 </li></ul><ul><li>Multiply each side by the inverse of 2 5 : </li></ul><ul><li>5 • 2n = 3 • 5 </li></ul><ul><li>2 5 7 2 </li></ul><ul><li>n = 15 </li></ul><ul><li>14 </li></ul>
  11. 11. Your Turn: <ul><li>Solve the following equations with one step (show your work!!): </li></ul><ul><li>r + 4 = 17 </li></ul><ul><li>g - 15 = -11 </li></ul><ul><li>13 + p = - 9 </li></ul><ul><li>-5b = 85 </li></ul><ul><li>- 7v = - 91 </li></ul><ul><li>w = -2 </li></ul><ul><li>3 9 </li></ul>
  12. 12. Answers: <ul><li>r = 13 </li></ul><ul><li>g = 4 </li></ul><ul><li>p = - 22 </li></ul><ul><li>b = - 17 </li></ul><ul><li>v = 13 </li></ul><ul><li>w = - 2/3 </li></ul>
  13. 13. Word Problems with One Step Equations <ul><li>You will need to know how to solve word problems involving these equations, by using the four-step problem solving plan: </li></ul><ul><li>Explore the problem </li></ul><ul><li>Plan the solution </li></ul><ul><li>Solve the problem </li></ul><ul><li>Examine the solution </li></ul>
  14. 14. 1. Explore the problem <ul><li>First, read the problem carefully, then: </li></ul><ul><li>Identify what information is given </li></ul><ul><li>Identify what you are asked to find </li></ul>
  15. 15. 2. Plan the Solution <ul><li>Choose a variable to represent the unknown that you are trying to solve for </li></ul><ul><li>Create an algebraic equation for solving </li></ul>
  16. 16. <ul><li>Solve the Problem </li></ul><ul><li>use algebraic methods </li></ul><ul><li>Show your work! </li></ul><ul><li>Examine the Solution </li></ul><ul><li>Is your answer “reasonable” ? </li></ul><ul><li>Did you check your work to be sure? </li></ul>
  17. 17. Let’s try it! <ul><li>Read the following: </li></ul><ul><li>One mile is equal to approximately 1.6 kilometers. A local running club is holding a 10 kilometer race. What is the length of the race in miles? </li></ul><ul><li>Define aVariable Let m = the number of miles </li></ul><ul><li>1.6 • m = 10 </li></ul><ul><li>Divide both sides by 1.6 (calculators ok) </li></ul><ul><li>m = 6.25 </li></ul><ul><li>The length of the race is 6.25 miles. </li></ul>
  18. 18. One more ! <ul><li>Write an Equation and Solve the Problem: </li></ul><ul><li>Noah received a paycheck on Friday. After buying some athletic shoes for $112, he had $96 left. </li></ul><ul><li>How much was his paycheck? </li></ul><ul><li>Let p = paycheck </li></ul><ul><li>p - 112 = 96 </li></ul><ul><li>+ 112 +112 </li></ul><ul><li>p = 208 </li></ul><ul><li>Noah’s paycheck was $208. </li></ul>
  19. 19. Homework: <ul><li>One step equation worksheet: </li></ul><ul><li>You MUST show your work to get credit on this assignment!!! </li></ul>

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