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Algebra 5 Point 5
 

Algebra 5 Point 5

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    Algebra 5 Point 5 Algebra 5 Point 5 Presentation Transcript

    • 5.5 Using Inequalities
      Objective:
      • To solve problems by using inequalities
      Frameworks: 10.P.1, 10.P.7
    • Translations
    • Can a number ever be . . .
      = x AND > x?
      = x AND < x?
      > x AND < x?
    • Trichotomy Property
      For all real numbers a and b, exactly one of the following three statements is true:
      a < b a = b a > b
    • Trichotomy Property in action
      Suppose that the number of books in Jane’s collection is at least 30.
      Then the number of books is not less than 30. By the Trichotomy Property, there are 2 remaining possibilities:
      the number of books is equal to 30
      the number of books is greater than 30
      “at least” translates to “≥”
    • Translate:
      Roberto weighs no less than 125 lb.
      r ≥ 125
      Jesse has between 20 and 30 books
      20 < b < 30
      John has at most $28.
      d ≤ 28
    • Mr. Smith rented a car for $39 a day plus $.20 a mile.
      How far can he drive in one day if he wants to spend at most $100?
      39 + .20m ≤ 100
      .20m ≤ 61
      m ≤ 305
    • The sum of 2 consecutive positive integers is at most 24. Find the integers.
      x first integer
      x + 2 second integer
      x + x + 2 ≤ 24 and x > 0 and x is odd
      2x≤ 22 and x > 0 and x is odd
      x ≤ 11 and x > 0 and x is odd
      Possible pairs:
      1,3 3,5 5,7 7,9 9,11 11,13
    • Turn to page 187
      Do 1-8