Nov. 17 Rational Inequalities

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Nov. 17 Rational Inequalities

  1. 1. Inequality 1
  2. 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. 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. 4. x ­ 1  The graph of       y = (x ­ 2)(x + 3) < 0 4
  5. 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. 6. Graph of                  y  = x2 ­ 2x ­ 8 x ­ 1 6
  7. 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. 8
  9. 9. Absolute Value Inequality Graph y = x Graph  y =   x 9
  10. 10. Graph y = x + 5 What will graph of   y =   x + 5    look like?  10
  11. 11. 11
  12. 12. 12
  13. 13. 13
  14. 14. Solve graphically x ­ 2 < _ 5 14
  15. 15. Solve algebraically x ­ 2 < _ 5 15
  16. 16. x + 1 _ < 3 2 16
  17. 17. x Solve algebraically + 1 _ < 3 2 17
  18. 18. Exercise 28 questions  6  ­  12 18

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