1. <
>
<
<
Inequalities
<
<
<
>

2. ≥ : greater than or equal to
An inequality is like an equation, but instead of an equal sign (=) it has one of these signs:
< : less than
≤ : less than or equal to
> : greater than
≥ : greater than or equal to

3. What do Inequalities mean?
A mathematical sentence that uses one of the inequality symbols to state the relationship between two quantities.

4. Graphing Inequalities
When we graph an inequality on a number line we use open and closed circles to represent the number.
The open circle indicates that the solution is less than or greater than that value.
The closed circle indicates that number is also part of the solution.
The line moves in the direction the arrow is pointing.
<
<
Plot an open circle ≤ ≥
Plot a closed circle

5. x < 5
means that whatever value x has, it must be less than 5. Try to name ten numbers that are less than 5!

6. Numbers less than 5 are to the left of 5 on the number line.5 10 15
-20
-15
-10 -5
-25 20 25
If you said 4, 3, 2, 1, 0, -1, -2, -3, etc., you are right.
There are also numbers in between the integers, like 2.5, 1/2, -7.9, etc.
The number 5 would not be a correct answer, though, because 5 is not less than 5.

7. x ≥ -2
means that whatever value x has, it must be greater than or equal to -2. Try to name ten numbers that are greater than or equal to -2

8. Numbers greater than -2 are to the right of -2 on the number line.5 10 15
-20
-15
-10 -5
-25 20 25 -2
If you said -1, 0, 1, 2, 3, 4, 5, etc., you are right.
There are also numbers in between the integers, like -1/2, 0.2, 3.1, 5.5, etc.
The number -2 would also be a correct answer, because of the phrase, “or equal to”.

9. Choose the correct graph that best describes each inequality.

10. Choose the correct graph that best describes each inequality.

11. Choose the correct graph that best describes each inequality.

12. Choose the correct graph that best describes each inequality.

13. Choose the correct solution that best describes each graph.

14. Choose the correct solution that best describes each graph.

15. Choose the correct solution that best describes each graph.

16. Choose the correct solution that best describes each graph.

17. Solving an Inequality
Follow the same rules and steps that we used to solve an equation.
Always undo addition or subtraction first, then multiplication or division.
Remember whatever is done to one side of the inequality must be done to the other side. The goal is to get the variable by itself.

18. Solve & Graph 1-Step Inequalities

19. Solve an Inequality w + 5 < 8 - 5 -5 w < 3
w < 3
All numbers less than 3 are solutions to this problem! 5 10 15
-20
-15
-10 -5
-25 20 25

20. More Examples 8 + r ≥ -2 -8 -8 r - 10 ≥ r
All numbers greater than-10 (including -10) ≥ 5 10 15
-20
-15
-10 -5
-25 20 25

21. More Examples 2x > -2 2 2 x > -1
x > -1
All numbers greater than -1 make this problem true! 5 10 15
-20
-15
-10 -5
-25 20 25

22. Solve each inequality and circle the possible solutions.

23. Solve each inequality and circle the possible solutions

24. Solve each inequality and circle the possible solutions

25. Solve each inequality and circle the possible solutions

26. Select the best graph.

27. Select the best graph.

28. Select the best graph.

29. Select the best graph.

30. Solve and Graph each inequality.

31. Solve and Graph each inequality.

32. Solve and Graph each inequality.

33. Solve and Graph each inequality.

34. Solve & Graph 2-Step Inequalities

35. All numbers less than 8 (including 8)
More Examples
2h + 8 ≤ 24
2h ≤ 16
h ≤ 8
All numbers less than 8 (including 8) 5 10 15
-20
-15
-10 -5
-25 20 25

36. Circle the possible solutions.

37. Circle the possible solutions.

38. Circle the possible solutions.

39. Circle the possible solutions.

40. Select the correct graph.

41. Select the correct graph.

42. Select the correct graph.

43. Select the correct graph.

44. Solve and graph the inequality.

45. Solve and graph the inequality.

46. Solve and graph the inequality.

47. Solve and graph the inequality.

48. x + 3 > -4 x > -7 6d > 24 d > 4 2x - 8 < 14 x < 11
QUIZ
Solve the inequality and graph the answer.
x + 3 > -4
6d > 24
2x - 8 < 14
2c – 4 < 2
x > -7
d > 4
x < 11
c < 3

51. Inequality Word Problems
At least ≤
At most ≥
No more than ≥
No less than ≤
Greater than >
More than >
Less than <
Greater than or equal to ≥
More than or equal to ≥
Less than or equal to ≤
Minimum ≤
Maximum ≥

52. Write the inequality to match the phrase

53. Write the inequality to match the phrase

54. Write the inequality to match the phrase

55. Write the inequality to match the phrase

56. Write the inequality to match the phrase

57. Write and Solve each word problem with an inequality.
The cost of a gallon of orange juice is $ What is the maximum number of containers you can buy for $15?
Sam has 3 bottles of water. Together, Sam and Dave have at most 12 bottles of water. Let x represent the number of bottles Dave has.
You want to rent a limousine for a trip to the city. The limo costs $700 for the night and $0.15 per mile. You have $750 to spend. Write an inequality that represents this scenario. How many miles can the limo travel?
Mark's Canoes rents canoes for $20 plus $35 per hour. You do not want to spend more than $150. For how many hours can you afford to rent the canoe?
Charles is saving $5 each week. He earns an extra $15 by mowing his neighbor's lawn. How many weeks will he need to save in order to have at least $75?

58. Write and Solve each word problem with an inequality.