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# Algebra 5 Point 5

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### Algebra 5 Point 5

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