1. Pre-Calculus Lesson 7: Solving Inequalities Linear inequalities, compound inequalities, absolute value inequalities, interval notation

2. Number Line are shown with open circles x<2x>4

3. Number Line are shown with open circles x<2x>4

4. Number Line are shown with open circles x<2x>4

5. Number Line  and  are shown with closed circles x  2x  4

6. Number Line  and  are shown with closed circles x  2x  4

7. Number Line  and  are shown with closed circles x  2x  4

8. Multiplication Property of Inequality When multiplying or dividing by a negative number, FLIP the INEQUALITY SIGN!

9. Example:

14. Compound Inequalities

15. Conjunction Example #1 -3-2 -1 0 1 2

16. Conjunction Example #1 -3-2 -1 0 1 2

17. Conjunction Example #1 -3-2 -1 0 1 2

18. Conjunction Example #1 -3-2 -1 0 1 2

19. Conjunction Example#2 6 7 8 9 10 11

20. Conjunction Example#2 6 7 8 9 10 11

21. Conjunction Example#2 6 7 8 9 10 11

22. Disjunction Example#1 0 1 2 3 4 5 6 7 8 9 10

23. Disjunction Example#1 0 1 2 3 4 5 6 7 8 9 10

24. Disjunction Example#2 -5 -4 -3 -2 -1 0 1 2 3 4 5

25. Disjunction Example#2 -5 -4 -3 -2 -1 0 1 2 3 4 5

26. Disjunction Example#2 -5 -4 -3 -2 -1 0 1 2 3 4 5

27. Absolute Value Inequalities

28. “Less Than” Rewrite the inequality as a conjunction. -a < x < a Solve.

29. -4 -3-2 -1 0 1 2 Example

30. -4 -3-2 -1 0 1 2 Example

31. -4 -3-2 -1 0 1 2 Example

32. -4 -3-2 -1 0 1 2 Example

33. “Greater Than” Rewrite the inequality as a disjunction. x a Solve.

34. Example -5 -4 -3 -2 -1 0 1 2 3 4 5

35. Example -5 -4 -3 -2 -1 0 1 2 3 4 5

36. Example -5 -4 -3 -2 -1 0 1 2 3 4 5

37. Example -5 -4 -3 -2 -1 0 1 2 3 4 5

38. Interval Notation  When using interval notation:  ( means "not included" or "open".  [ means "included" or "closed".  The inequality would be written as the interval  The inequality  would be written as the interval

39. Which statement below is the correct interval notation for the situation depicted in this number line graph? http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

40. Which statement below is the correct interval notation for the situation depicted in this number line graph? http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

41.  Write the following statement as an inequality:  x 4 http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

42.  Write the following statement as an inequality:  x 4 http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

43.  Write the following inequality as interval notation: -2 1 http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

44.  Write the following inequality as interval notation: -2 1 http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

45. Practice Questions Solve each inequality, express the answer in interval notation, and graph the solution on the number line. 1. 2. 3. 4. 5.