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3.5 And 3.6 Solving Equations
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3.5 And 3.6 Solving Equations

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

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