1. Solving Inequalities by Addition and Subtraction
Algebra 1 Notes Lesson 6-1
Solving Inequalities by Addition and Subtraction

2. Mathematics Standards
Number, Number Sense and Operations: Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities.
Patterns, Functions and Algebra: Generalize patterns using functions or relationships, and freely translate among tabular, graphical and symbolic representations.
Patterns, Functions and Algebra: Add, subtract, multiply and divide monomials and polynomials.
Patterns, Functions and Algebra: Write and use equivalent forms of equations and inequalities in problem situations.

3. Addition Property of Inequalities
For all numbers a, b, and c, the following are true:
1. If a > b, then a + c > b + c.
2. If a < b, then a + c < b + c.

4. Example 1 Solve 12 ≥ y – 9. Then graph it on a number line. 12 ≥ y – 9
21 ≥ y

5. Example 1 Solve 12 ≥ y – 9. Then graph it on a number line. 12 ≥ y – 9
21 ≥ y or y ≤ 21

6. Example 1 Solve 12 ≥ y – 9. Then graph it on a number line. 12 ≥ y – 9
21 ≥ y or y ≤ {y | y ≤ 21}

7. {y | y ≤ 21}
Set builder notation
| reads “such that”

8. Example 1 Solve 12 ≥ y – 9. Then graph it on a number line. 12 ≥ y – 9
21 ≥ y or y ≤ {y | y ≤ 21}

9. Subtraction Property of Inequalities
For all numbers a, b, and c, the following are true:
1. If a > b, then a – c > b – c.
2. If a < b, then a – c < b – c.

10. Example 2 Solve 12n – 4 ≤ 13n. Then graph it on a number line.

11. Example 2 Solve 12n – 4 ≤ 13n. Then graph it on a number line.
-4 ≤ n or {n | n ≥ -4}

12. Example 2 Solve 12n – 4 ≤ 13n. Then graph it on a number line.
-4 ≤ n or {n | n ≥ -4}

13. > < > < Is at most Is less than is fewer than
> < > <
Is at most
Is less than is fewer than
Is no less than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

14. > < > < Is at most Is less than is fewer than
> < > <
Is at most
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Is no less than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

15. > < > < Is at most Is less than is fewer than
> < > <
Is at most
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Is no less than
Is greater than Is more than
or equal to
Is at least
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equal to
Is no more than

16. > < > < Is at most Is less than is fewer than
> < > <
Is at most
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Is no less than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

17. > < > < Is less than Is at most is fewer than
> < > <
Is less than Is at most
is fewer than
Is no less than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

18. > < > < Is less than Is at most is fewer than
> < > <
Is less than Is at most
is fewer than
Is no less than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

19. > < > < Is less than Is at most Is no less than
> < > <
Is less than Is at most
is fewer than
Is no less than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

20. > < > < Is less than Is at most Is no less than
> < > <
Is less than Is at most
is fewer than
Is no less than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

21. > < > < Is less than Is no less than Is at most
> < > <
Is less than Is no less than Is at most
is fewer than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

22. > < > < Is less than Is no less than Is at most
> < > <
Is less than Is no less than Is at most
is fewer than
Is greater than Is more than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

23. > < > < Is less than Is no less than Is at most
> < > <
Is less than Is no less than Is at most
is fewer than Is greater than
or equal to
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Is at least
Is greater than Is less than or
equal to
Is no more than

24. > < > < Is less than Is no less than Is at most
> < > <
Is less than Is no less than Is at most
is fewer than Is greater than
or equal to
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Is at least
Is greater than Is less than or
equal to
Is no more than

25. > < > <
Is more than Is less than Is no less than Is at most
is fewer than Is greater than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

26. > < > <
Is more than Is less than Is no less than Is at most
is fewer than Is greater than
or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

27. > < > <
Is more than Is less than Is no less than Is at most
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or equal to
Is at least
Is greater than Is less than or
equal to
Is no more than

28. > < > <
Is more than Is less than Is no less than Is at most
is fewer than Is greater than
or equal to
Is at least
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equal to
Is no more than

29. > < > <
Is more than Is less than Is no less than Is at most
Is greater than is fewer than Is greater than
or equal to
Is at least
Is less than or
equal to
Is no more than

30. > < > <
Is more than Is less than Is no less than Is at most
Is greater than is fewer than Is greater than
or equal to
Is at least
Is less than or
equal to
Is no more than

31. > < > <
Is more than Is less than Is no less than Is at most
Is greater than is fewer than Is greater than Is less than or
or equal to equal to
Is at least
Is no more than

32. > < > <
Is more than Is less than Is no less than Is at most
Is greater than is fewer than Is greater than Is less than or
or equal to equal to
Is at least
Is no more than

33. > < > <
Is more than Is less than Is no less than Is at most
Is greater than is fewer than Is greater than Is less than or
or equal to equal to
Is at least Is no more than

34. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.

35. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) +

36. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) +

37. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) + x

38. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) + x <

39. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) + x < 5

40. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) + x < 5
x < 5

41. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) + x < 5
x < 5
x < 5

42. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) + x < 5
x < 5
x < 5

43. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) + x < 5 x < 1.50
x < 5
x < 5

44. Write an inequality and solve
I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.
2(1) + 3(0.50) + x < 5 x < 1.50
x < 5 Only if the sugar stick
x < 5 is at most $1.50

45. Example 3
Write an inequality for the sentence below. Then solve the inequality.
Seven times a number is greater than six times that number minus two. 7n

46. Example 3
Write an inequality for the sentence below. Then solve the inequality.
Seven times a number is greater than six times that number minus two.
7n >

47. Example 3
Write an inequality for the sentence below. Then solve the inequality.
Seven times a number is greater than six times that number minus two.
7n > 6n

48. Example 3
Write an inequality for the sentence below. Then solve the inequality.
Seven times a number is greater than six times that number minus two.
7n > 6n – 2
-6n -6n
n > -2

49. Example 3
Write an inequality for the sentence below. Then solve the inequality.
Seven times a number is greater than six times that number minus two.
7n > 6n – 2
-6n -6n
n > -2 {n | n > -2}

50. Example 4
5x + 7 > 6

51. Example 4
5x + 7 > 6

52. Example 4
5x + 7 > 6
5x > -1

53. Example 4
5x + 7 > 6
5x > -1

54. Example 4
5x + 7 > 6
5x > -1
x > -⅕

55. Example 4 5x + 7 > 6 {x | x > -⅕} - 7 -7 5x > -1 5 5
5x > -1
x > -⅕

56. Example 4 5x + 7 > 6 {x | x > -⅕} - 7 -7 5x > -1 5 5 -⅖ -⅕ 0
5x > -1
⅖ -⅕ 0
x > -⅕

57. Example 4 5x + 7 > 6 {x | x > -⅕} - 7 -7 5x > -1 5 5 -⅖ -⅕ 0
5x > -1
⅖ -⅕ 0
x > -⅕

58. Example 4 5x + 7 > 6 {x | x > -⅕} - 7 -7 5x > -1 5 5 -⅖ -⅕ 0
5x > -1
⅖ -⅕ 0
x > -⅕

59. Homework
Pg 321
14-50 Evens
Omit 38
Use Set Builder AND
Number Lines