3.5 And 3.6 Solving Equations

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October 2nd, 2008 Lecture Notes. Solving one-step equations.

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  • Thanks so much for this great Presentation on equations. I have feautured it as an embed on my student help website here:
    http://passyworldofmathematics.wordpress.com/2011/10/20/equations-word-problems/ .
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3.5 And 3.6 Solving Equations

  1. 1. Section 3.5: Solving Equations by Adding or Subtracting By Ms. Dewey-Hoffman October 2 nd , 2008 (Thursday)
  2. 2. Using Subtraction to Solve Equations. <ul><li>Remember these? N + 27 = 10? </li></ul><ul><li>The reason we can solve this type of problem is because of the Subtraction Property of Equality. </li></ul><ul><li>Remember! Subtract the same number from each side of the equation. </li></ul><ul><li>This will keep things balanced. </li></ul><ul><li>Check your work by sticking your answer back in to the original problem. </li></ul>
  3. 3. Try This, Then Check: <ul><li>Solve: </li></ul><ul><li>n + 4.5 = -9.7 </li></ul><ul><li>- 4.5 -4.5 </li></ul><ul><li>n + 0 = -14.2 </li></ul><ul><li>n = -14.2 </li></ul><ul><li>Now check: </li></ul><ul><li>-14.2 + 4.5 = -9.7 </li></ul><ul><li>This statement is true. </li></ul><ul><li>n = -14.2 </li></ul>
  4. 4. Try This, Then Check: <ul><li>Solve: </li></ul><ul><li>x + 4.9 = 18.8 </li></ul><ul><li> - 4.9 = - 4.9 </li></ul><ul><li>x + 0 = 13.9 </li></ul><ul><li>x = 13.9 </li></ul><ul><li>Check! </li></ul><ul><li>13.9 + 4.9 = 18.8 </li></ul><ul><li>This is a true statement. </li></ul><ul><li>x = 13.9 </li></ul>
  5. 5. Subtraction Property of Equality <ul><li>Instead of using mental math, especially for crazy decimals, we use the Subtraction Property of Equality to help us solve for unknown variables. </li></ul><ul><li>So…DON’T ASK ABOUT MENTAL MATH and NO EXCUSE FOR NOT SHOWING WORK! </li></ul>
  6. 6. Word Problem with Subtraction Property of Equality <ul><li>A communications satellite is circling Earth. Find the approximate distance from the satellite to the moon. </li></ul>239.9 Thousand Miles 22.3 Thousand Miles ???
  7. 7. Word Problem with Subtraction Property of Equality, Cont. <ul><li>Our Equation looks like this: 22.3 + x = 239.9 </li></ul><ul><li>22.3 is miles from Earth to Satellite. </li></ul><ul><li>X is the miles from Satellite to Moon. </li></ul><ul><li>239.9 is the miles from the Earth to Moon. </li></ul>239.9 Thousand Miles 22.3 Thousand Miles ???
  8. 8. Word Problem with Subtraction Property of Equality, Solve. <ul><li>22.3 + x = 239.9 </li></ul><ul><li>-22.3 -22.3 </li></ul><ul><li>0 + x = 217.6 </li></ul>239.9 Thousand Miles 22.3 Thousand Miles 218 Thousand Miles <ul><li>0 + x = 217.6 </li></ul><ul><li>X = 217.6 miles from Satellite to Moon. </li></ul><ul><li>Round: 218 thousand miles from Satellite to Moon. </li></ul>
  9. 9. Another Word Problem <ul><li>A store’s cost (plus) markup is the price you pay for an item. Suppose a pair of shoes costs a store $35.48. You pay $70. Write and solve an equation to find the store’s markup. </li></ul><ul><li>Store pays $35.48 for a pair of shoes. </li></ul><ul><li>You pay $70.00 </li></ul><ul><li>What is the markup (what the store adds) to the cost of the shoes to make it what you paid? </li></ul>
  10. 10. Shoe Store Markup <ul><li>Store pays $35.48 for a pair of shoes. </li></ul><ul><li>You pay $70.00 </li></ul><ul><li>What is the markup (what the store adds) to the cost of the shoes to make it what you paid? </li></ul><ul><li>$35.48 + M = $70.00 </li></ul><ul><li>Go ahead and do it! </li></ul><ul><li>M = $34.54, is the markup the store puts on the shoes. </li></ul><ul><li>So, the store makes $34.54 profit off of your $70 purchase. </li></ul>
  11. 11. Using Addition Property of Equality to Solve Equations. <ul><li>Remember! Add the same number from each side of the equation. </li></ul><ul><li>This will keep things balanced. </li></ul><ul><li>Check your work by sticking your answer back in to the original problem. </li></ul>
  12. 12. Sample Problem <ul><li>K – 14.4 = -18.39 </li></ul><ul><li>+ 14.4 = +14.4 </li></ul><ul><li>K – 0 = -3.99 </li></ul><ul><li>K = -3.99 </li></ul><ul><li>N – 5.85 = 15.25 </li></ul><ul><li>+ 5.85 = +5.85 </li></ul><ul><li>N – 0 = 21.1 </li></ul><ul><li>N = 21.1 </li></ul><ul><li>-10 = C – 2.6 </li></ul><ul><li>+2.6 +2.6 </li></ul><ul><li>-7.4 = C – 0 </li></ul><ul><li>-7.4 = C </li></ul>
  13. 13. Word Problem! <ul><li>Danzel wrote a check for $76.85. His new account balance is $235.00. What was his previous balance? </li></ul>Previous Balance - Check = New Balance Previous Balance $76.85 - = $235.00 + 76.85 + 76.85 Previous Balance = $311.85
  14. 14. Solving Equations by Multiplying or Dividing Decimals Section 3.6 By Ms. Dewey-Hoffman
  15. 15. Using Division to Solve Equations <ul><li>Division undoes multiplication. </li></ul><ul><li>You can solve an equation involving multiplication by dividing. </li></ul><ul><li>0.9r = - 5.4 </li></ul><ul><li>0.9 0.9 </li></ul><ul><li>r = - 6 </li></ul><ul><li>Now check it! </li></ul><ul><li>r = - 6 </li></ul><ul><li>0.9r = - 5.4 </li></ul><ul><li>0.9(-6) = -5.4 </li></ul>
  16. 16. Word Problem <ul><li>An oil field produces an average of 16.8 thousand barrels of crude oil per day. About how many days will it take to produce 200 thousand barrels? </li></ul>Barrels Made In A Day X Number of Days = 200 Thousand Barrels 16.8 X Number of Days = 200 Thousand Barrels
  17. 17. Word Problem Barrels Made In A Day X Number of Days = 200 Thousand Barrels 16.8 X Number of Days = 200 Thousand Barrels  16.8  16.8 Number of Days = 11.904, round to 12 Days. It will take 12 days to make 200 barrels of oil.
  18. 18. Using Multiplication to Solve Equations <ul><li>To solve an equation involving division, multiply each side by the same nonzero number. </li></ul><ul><li>M  -7.2 = -12.5 </li></ul><ul><li>x –7.2 x –7.2 </li></ul><ul><li>M = 90 </li></ul><ul><li>Now Check! </li></ul><ul><li>M = 90 </li></ul><ul><li>M  -7.2 = -12.5 </li></ul><ul><li>90  -7.2 = -12.5 </li></ul><ul><li>True Statement </li></ul>
  19. 19. When Solving Equations… <ul><li>Do everything you just learned, but remember! </li></ul><ul><li>You’re trying to get the variable alone, by itself, on one side of the equal side. </li></ul><ul><li>Whatever is happening to your variable, you have to undo. </li></ul><ul><li>If its multiplying, you divide. </li></ul><ul><li>If its subtracting, you add. </li></ul><ul><li>If its adding, you subtract. </li></ul><ul><li>If its dividing, you multiply. </li></ul>
  20. 20. Assignment #18 <ul><li>Handout Practice 3.5 and 3.6, Both Sides, ALL. </li></ul><ul><li>Make sure you bring your notes tomorrow. </li></ul>

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