1. Solving Inequalities Equations

3. If you read from left to right 10 “is greater than “ 5 X

4. If you read from right to left 5 “is less than “ 10 X

6. If you read from left to right 5 “is less than “ 10 X

7. If you read from right to left 10 “is greater than“ 10 X

8. . Number line X is equal to 7
Therefore you include the 7 with a dotted cirle.

9. Number line .

10. . Number line X is equal to -3
Therefore you include the -3 with a dotted circle.

11. Number line .

12. . Number line X is greater equal to -2
Therefore you include the -2 with a dotted circle.
You draw and arrow to the right

13. Number line .

14. O Number line X is greater than 2
Therefore you do not include the 2 with an open circle.
You draw and arrow to the right

15. Number line O

16. . Number line X is less than equal to -6
Therefore you include the -6 with an dotted closed circle
You draw and arrow to the left

17. Number line .

18. O Number line X is less than -6
Therefore you do not include the -6 with an open circle
You draw and arrow to the left

19. Number line O

20. > Greater Than Equal To
Inequality Symbols
Open Circle indicates Not Equal
> Greater Than
> Greater Than Equal To
Closed Circle indicates Equal To
< Less Than
Open Circle indicates Not Equal
< Less Than Equal to
Closed Circle indicates Equal To

21. Solving Inequality Equations
X + 5 = 13
What Side of the equation you are going to work with ?
The Rights side
The lefts side

22. Solving Inequality Equations
X + 5 > 13
What Side of the equation you are going to work with ?
The Rights side
The lefts side

23. Solving Inequality Equations
X + 5 > 13
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

24. Solving Inequality Equations
X + 5 > 13 -5 -5
_________
You subtract – 5 in both side of the equatiion .

25. Solving Inequality Equations
X + 5 > 13
_________ X
> 8
You drop down the X.
Cancel 5
Drop down “>“ sign.
And then subtract 13 – 5 = 8.

26. Solving Inequality Equations
X + 5 > 13 .
_________ X
> 8
X is Greater than equal to 8
Therefore you include the 8 with a closed circle
You draw and arrow to the right

27. Solving Inequality Equations
2x < 18
What Side of the equation you are going to work with ?
The Rights side
The lefts side

28. Solving Inequality Equations
2x < 18
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

29. Solving Inequality Equations
___
2x < 18 __
_________ 2 2 1 x 9
<
You divide by 2 in both side.
Now 2 divide 2 gives you 1 x.
You drop down “ <“
Now add gives you 9. ÷

30. Solving Inequality Equations
___
2x < 18 __
_________ 2 2 1 x 9
< O
X is Less than 9
Therefore you do not include the 9 with an opened circle
You draw and arrow to the left

31. Solving Inequality Equations
x 4
> - 2
What Side of the equation you are going to work with ?
The Rights side
The lefts side

32. Solving Inequality Equations
x 4
> - 2
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

33. Solving Inequality Equations
x 4 4•
> - 2 •4
___________ 1 x
> -8
You multiply by 4 in both side.
Now 4 divide 4 gives you 1X.
You drop down “>“
Now -2 multiply by 4 equals -8.

34. Solving Inequality Equations
x 4 4•
> - 2 •4 .
___________ 1 x
> -8
X is Greater equal to -8
Therefore you do include the -8 with an closed circle
You draw and arrow to the right

35. In Inequalities there are two cases you Need to Flip The Sign

36. When you multiply or divide by a negative number
Flip the Sigh of Inequality

37. Solving Inequality Equations
- 5X - 3 > 12
What Side of the equation you are going to work with ?
The Rights side
The lefts side

38. Solving Inequality Equations
- 5X - 3 > 12
What Side of the equation you are going to work with ?
The lefts side
…Because that’s where the variable is.

39. Solving Inequality Equations
- 5X - 3 > 12
___________ +3 +3
-5X
> 15
You add by 3 in both side.
You drop down -5x
Cancel 3
You drop down >
Now 12 plus 3 gives you 15.

40. Solving Inequality Equations
- 5X - 3 > 12
___________ +3 +3
-5X
> __ 15 __ -5 -5
___________ 1 x
<
- 3
Now divide by -5 in both sides
Now -5 divide -5 gives you 1X.
You drop down “ >“ and flip the sign
Now 15 divide by 5 equals -3

41. Solving Inequality Equations
- 5X - 3 > 12
___________ +3 +3
-5X
> __ 15 __ -5 -5
___________ 1 x
<
- 3 O

42. Second Case when you flip the Inequalities Sign
When the variable is in the right side of the equation
Change it to the left side. X

43. Second Case when you flip the Inequalities Sign
When the variable is in the right side of the equation
Change it to the left side. X
And Flip the sign

44. Solving Inequality Equations
- 44 < X +8 +8
___________ 6X 36
<
You add + 8 in both side.
Now -44 plus 8 gives you -36.
You drop down “ < “
Cancel 8
Now You drop down 6x

45. Solving Inequality Equations
- 44 < X
___________ +8 +8 6X 36 __
< __
___________ 6 6 6
< 1 X
Now divide by 6 in both sides
Now 36 divide 6 gives you 6.
Drop < and 6 divide 6 gives you 1X.

46. Solving Inequality Equations
- 44 < X
___________ +8 +8 6X 36 __
< __
___________ 6 6 6
< 1 X

47. Solving Inequality Equations
- 44 < X
___________ +8 +8 6X 36 __
< __
___________ 6 6 6
< X

48. Solving Inequality Equations
- 44 < X
___________ +8 +8 6X 36 __
< __
___________ 6 6
> 6 X

49. Solving Inequality Equations
- 44 < X
___________ +8 +8 6X 36 __
< __ .
___________ 6 6
> 6 X

50. Compound Inequalities
A compound inequality consists of two inequalities that are joined together by the word "and" or the word "or".
x > -3 and x < 5

51. Compound Inequalities
A compound inequality consists of two inequalities that are joined together by the word "and" or the word "or".
x > -3 and x < 5

52. Compound Inequalities
x > -3 and x < 5

53. Compound Inequalities
x > -3 and x < 5
X>-3 O
X<5 O

54. Compound Inequalities
x > -3 and x < 5
X>-3 O
X<5 O O O

55. Compound Inequalities
x > -3 and x < 5
X>-3 O
X<5 O O O

56. Compound Inequalities
x > -3 and x < 5 O O

57. Compound Inequalities
x < -3 or x > 5
X<-3
X > 5 O O
NO SOLUTION

58. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16
Solve the Two Inequalities Independently

59. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16
Solve the Two Inequalities Independently
10< 2x + 8
and
2x + 8< 16

60. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16
10< 2x + 8
and
2x + 8< 16

61. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16
10< 2x + 8
2x + 8< 16
and
______
______ 2
< 2x 2x
< 8 __ __ __ __
______
______ 2 2 2 2 4 1
< x
< x x
> 1

62. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16
10< 2x + 8
2x + 8< 16
and
______
______ 2
< 2x 2x
< 8 __ __ __ __
______
______ 2 2 2 2 4 1
< x
< x x
> 1

63. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16 x
< 4 x
> 1

64. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16 O

65. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16 O . O

66. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16 O . O

68. Compound Inequalities - Example 1
Solve and Graph the following Inequality
10< 2x + 8< 16
10< 2x + 8
2x + 8< 16
and
______
______ 2
< 2x 2x
< 8 __ __ __ __
______
______ 2 2 2 2 4 1
< x
< x x
> 1