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

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Algebra 5 Point 5

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