1. 4.3 Properties of inequalities Date: 11/13/18
1. Grab your Binder 2. Copy down the Essential Question (EQ). 3. Work on the Warm-up.
Essential Question
How is an inequality different from an equation?
Warm Up
<
<
<
> =
<

2. Basics of Inequalities- vocabulary
Equal sign = Example: 4𝑥=8 we say 4𝑥 is equal to 8 Great Than > Example: 4>1 we say 4 is great than 1 Less Than < Example: 3<5 we say 3 is less than 5

3. Try it
2 9
−6 5
−12 −4
−8 8

4. Solution 2 < 9 2 is less than 9 5 > −6 5 is greater than -6
−8 = 8 −8 is equal to 8

5. Basics of Inequalities- vocabulary part 2
Great Than or equal to ≥ Example: 2𝑥≥4 2x is great than or equal to 4 Less Than or equal to ≤ Example: 3𝑥≤5 3x is less than or equal to 5

7. Review: Characteristics of Equal sign
An equal sign shows the balance between two sides If I add 2 to one side, I will need to add 2 to another side to maintain it’s balance.

8. Addition Property of Inequality
Adding the same number to each side of the inequality produces an equivalent inequality.
Subtraction Property of Inequality
Subtracting the same number to each side of the inequality produces an equivalent inequality.
Show interactive

9. Example One: Solve by Adding

11. Solutions to Guided practice

12. Set- builder notation

13. Graphing the set-builder notation
We graph single values on a number line

14. Example Three: Variable on each side
Solve then graph the solution set.

15. Solve then graph the solution set.

16. Solution

17. Solution

18. Discovery
Lets see what happen when we multiple each side of an inequality
Show interactive

19. Discovery
When you multiply by a negative value, the direction of the inequality changes
Show interactive

20. Example 2: Solve by Multiplying
Solve then graph the solution

21. Solve then graph the solution

22. Solutions

23. Solutions

24. Solutions

25. Solutions

26. Discovery
Lets see what happen when we divide each side of an inequality
Show interactive

27. Discovery
When you divide by a negative value, the direction of the inequality changes
Show interactive

28. Example 3: Divide to Solve an Inequality

29. Example 3: Divide to Solve an Inequality

30. Solve then graph the solution

31. Solve then graph the solution

32. Solve then graph the solution

33. Solve then graph the solution

34. Solve then graph the solution

35. 4.3 Properties of inequalities Part 2 Date: 11/14/18
1. Grab your Binder 2. Copy down the Essential Question (EQ). 3. Work on the Warm-up.
Essential Question
Why does the inequality flip when you divide or multiply by a negative value?
Warm Up
Describe and correct the error in determining whether 8 is in the solution set of the inequality.

56. Write the sentence as an inequality
Solutions
Write the sentence as an inequality
1. 𝑧−6≥11
2. 12 ≤−1.5𝑤+4

57. Write an inequality that represents the graph
Solutions
Write an inequality that represents the graph
3. { 𝑥 𝑥<0}
4. { 𝑥 𝑥≥8}

60. 4.4 Solving Multiple steps inequalities Date: 11/15/18
1. Grab your Binder 2. Copy down the Essential Question (EQ). 3. Work on the Warm-up.
Essential Question
How is the zero set different from the set of all real numbers?
Warm Up
Describe and correct the error in solving the inequality.

61. Spot the difference Solve −11𝑦>33 Solve −11𝑦−13>42
There are more numbers and terms in number 2.
You will have to do more steps to solve for y.
We called this, “ Solving multi-step Inequalities”

62. Remembering the Properties of Inequality
𝑥−2> Addition Property of Inequality 𝑥>6 𝑥+3>7 −3 −3 Subtraction Property of Inequality 𝑥>4

63. Remembering the Properties of Inequality
𝑥 2 >4 2∙ 𝑥 2 >4∙2 Multiplication Property of Inequality 𝑥>8 3𝑥> 𝑥> 12 3 Division Property of Inequality 𝑥>4

64. Remembering to change the direction of the Inequality
− 𝑥 2 >4 −2∙− 𝑥 2 <4∙−2Multiplication Property of Inequality Change the direction of the inequality 𝑥<−8 −3𝑥>−12 3 −3 𝑥< −12 −3 Division Property of Inequality 𝑥<4

65. Example 2 Inequality Involving a Negative Coefficient

67. Solutions

68. Solutions

69. Example 3 Write and Solve an Inequality

71. Review: The Distributive Property
4(3𝑡−5) Original expression 4 3𝑡 +4(−5) Distribute the 4 to each term inside the parenthesis −12t −20 Simplify

72. Example 4: Distributive Property

76. 5-35
Empty Set and All Reals

77. Connecting to Prior Knowledge
Review Problem: Solve this equation 9𝑡−5 𝑡−5 =4(𝑡−3)

79. What happen if it is an inequality
Solve this inequality 9𝑡−5 𝑡−5 ≤4(𝑡−3)

80. Do we say that there is “ no solutions”
We say the solution is the “ empty set”

81. What is the empty set
Definition Empty set : a list of values that contain nothing in it. Also called the null set Symbol { } or ∅ The empty does not contain zero in it. Zero is something. The empty set contains nothing in it.

82. Connecting to Prior Knowledge
Review Problem: Solve this equation 3 4𝑚+6 =42+6(2𝑚−4)

84. What happen if it is an inequality
Solve this equation 3 4𝑚+6 ≤42+6(2𝑚−4)

85. Do we say that there is “ infinite solution”
We say the solution is the“ Set of all real number”

86. What is the empty set
Definition Set of all Real Number: a list of values that contain all the real number Also called the All Real There is no Symbol

90. Solve each inequality. Graph each solution.
a. 𝑦 −6 +7<9 b. 2𝑣−4≥8

91. Solutions

92. Solutions

93. 4.3 Solving Multiple steps inequalities Date: 11/15/18
1. Grab your Binder 2. There is no Essential Question (EQ). 3. There is no Warm-up.
Essential Question
There is none
Warm Up
There is none.
Group Test

94. Group Test Work together to complete the test.
Show all work to get credit
IF you just have the answer then you will get the question wrong.
Staple all the work together as a group
2-3 people per group.