1. INEQUALITIES MATH10 ALGEBRA Inequalities(Algebra and Trigonometry, Young 2nd Edition, page 136-170)

3. Solve linear and nonlinear inequalities.

5. To classify inequalities as absolute or conditional.

6. To use interval and set notation in writing solutions to inequalities.

7. To represent graphically the solution to inequalities.

8. Toapply intersection and union concepts in solving compound inequalities.

9. To solve linear and fractional inequalities.

12. Week 5 Day 1 GRAPHING INEQUALITIES and INTERVAL NOTATION

14. set notation

15. interval notation

17. b is the right endpoint

18. If an inequality is a strict inequality (< or >) parenthesis is used.

20. Week 5 Day 1 Let x be a real number , x is …. ] or [ b a a a b a b ) a or ] or

21. Week 5 Day 1 Let x be a real number , x is …. or ( b b b b [ or R R

23. Negative infinity means continuing indefinitely to the left on the number line.

25. Week 5 Day 1 Example 2 x ≤ 4 (-∞,4] ] ● 0 4 -4 0 4 -4

26. Week 5 Day 1 Example 3 x > 4 (4, +∞) 0 4 -4 0 4 -4 ( ○

27. Week 5 Day 1 Example 4 x ≥4 [4, +∞) 0 4 -4 0 4 -4 [ ●

28. Week 5 Day 1 EXAMPLE 5 ) or [ 4 -1 4 -1

29. Week 5 Day 1 EXAMPLE 5 ] or [ 4 0 4 0

30. Week 5 Day 1 Example 6: Classroom example 1.5.1 page 137 Express the following as an inequality and an interval. x is less than -1 x is greater than or equal to 3 x is greater than -2 and less than or equal to 7.

31. DEFINITION Week 5 Day 1 UNION AND INTERSECTION

32. Week 5 Day 1 DOUBLE OR COMBINED INEQUALITY A statement formed by joining two clauses with the word and is called a conjunction. For a conjunction to be true, both clauses must be true. A statement formed by joining two clauses with the word or is called a disjunction. For a disjunction to be true, at least one of the clauses must be true.

33. Example Week 5 Day 1

34. Week 5 Day 1 SOLVING LINEAR INEQUALITIES

36. INEQUALITY PROPERTIES Week 5 Day 1 1. Interchanging the two sides of the inequality 2.Multiplying or dividing by the same negative number.

37. SOLVING A LINEAR INEQUALITY Week 5 Day 1 Example

38. SOLVING A LINEAR INEQUALITIES WITH FRACTION Week 5 Day 1 Example Note: Common mistake is using cross multiplication to solve fractional inequalities.

39. SOLVING A DOUBLE OR COMPOUND LINEAR INEQUALITY Week 5 Day 1 Example

41. Week 5 Day 2 NON LINEAR INEQUALITIES IN ONE VARIABLE

43. To solve polynomial inequalities.

44. To solve rational inequalities.

45. To solve absolute value inequalities

50. Week 5 Day 2 SOLVING A POLYNOMIAL INEQUALITY Solve each inequality:

53. Determine values that make the numerator or denominator equal to zero

54. Always exclude values that make the denominator = 0. Draw the number line with zeros labeled. Determine the sign of the polynomial in each interval. Identify which interval(s) make the inequality true. Write the solution in interval notation.

55. Week 5 Day 2 SOLVING A RATIONAL INEQUALITY Solve each inequality:

56. Week 5 Day 2 ABSOLUTE VALUE INEQUALITIES PROPERTIES OF ABSOLUTE VALUE INEQUALITIES

57. Week 5 Day 2 SOLVING AN ABSOLUTE VALUE INEQUALITY Solve each inequality:

58. APPLICATIONS INVOLVING LINEAR INEQUALITY Example

59. APPLICATIONS INVOLVING LINEAR INEQUALITY

61. Week 5 Day 2 CLASSWORK #s 85 page 144 #s 25 page 154 #s 43,49 page 162 HOMEWORK #s 69,83,86,89,91,99 pages 143-144 #s 10,13,19,28,38,44,55 page 154 #s 53,57,62 page 162