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Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
Nov. 17 Rational Inequalities
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Nov. 17 Rational Inequalities

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  • 1. Inequality 1
  • 2. Rational Inequality x ­ 1  Example < 0 (x ­ 2)(x + 3) 1. Simplify the rational expression so that zero is on one side  and the expression involving x is on the other side 2. Factor any quadratic expressions 3. Place critical numbers on a number line Critical Numbers: the zeros, and the values that make                the inequality undefined(non­permissible values) 4. Test points within each interval between the critical values, to  determine if the expression as a whole is positive or negative 5. State the intervals that qualify as solutions to the  inequality 2
  • 3. Solve the inequality x ­ 1  < 0 (x ­ 2)(x + 3) ­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10 3
  • 4. x ­ 1  The graph of       y = (x ­ 2)(x + 3) < 0 4
  • 5. Solve:  x2 ­ 2x ­ 8 > 0 _ x ­ 1 ­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10 5
  • 6. Graph of                  y  = x2 ­ 2x ­ 8 x ­ 1 6
  • 7. Solve x 1 > x ­ 3 x + 2 ­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10 7
  • 8. 8
  • 9. Absolute Value Inequality Graph y = x Graph  y =   x 9
  • 10. Graph y = x + 5 What will graph of   y =   x + 5    look like?  10
  • 11. 11
  • 12. 12
  • 13. 13
  • 14. Solve graphically x ­ 2 < _ 5 14
  • 15. Solve algebraically x ­ 2 < _ 5 15
  • 16. x + 1 _ < 3 2 16
  • 17. x Solve algebraically + 1 _ < 3 2 17
  • 18. Exercise 28 questions  6  ­  12 18

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