1. Inequalities by Graphing, Writing, Identifying & One Step Addition & Subtraction

2. Real World Application
1) How old are you?
Are you older than 6? a
> 6

3. Lesson Objectives
1) Graph, write and identify linear inequalities with one variable.
2) Solve one-step linear inequalities with addition and subtraction.

4. Definition What is an Inequality? Regular equation - usually has
1 solution.
1 solution.
3x + 6 = 18 3x
What is an Inequality?
– 6
– 6
– 6 3x
+ 0 = 12 3 3 3
x = 4 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

5. Definition What is an Inequality? Inequality equation - always
has more than 1 solution.
more than 1 solution.
3x + 6 < 18 3x
What is an Inequality?
– 6
– 6
– 6 3x
+ 0
< 12 3 3 3
x < 4 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

6. The numbers less than four is the answer. (3,2,1,…)
Definition
Inequality – is the value of elements of an ordered set. (Group of number)
x < 4
The numbers less than four is the answer. (3,2,1,…)

7. Rule
The rules of addition and subtraction properties of equations are the same with inequalities.

8. Rule <,> = when graphing inequalities have empty circles.
≤,≥ = when graphing inequalities have a filled circles.

9. Pacman eats the larger number. Is the variable bigger or smaller?
Example
2) Graph the inequality below.
Smaller
Bigger d d ≤ 5 5
Pacman eats the larger number.
Is the variable bigger or smaller?
Smaller
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

10. Pacman eats the larger number. Is the variable bigger or smaller?
Whiteboard Practice
3) Graph the inequality below.
Bigger
Smaller 4 4
> y y
Pacman eats the larger number.
Is the variable bigger or smaller?
Smaller
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

11. Pacman eats the larger number. Is the variable bigger or smaller?
Example
4) Graph the inequality below.
Smaller
Bigger x x
<
– 6
– 6
Pacman eats the larger number.
Is the variable bigger or smaller?
Smaller
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

12. Pacman eats the larger number. Is the variable bigger or smaller?
Whiteboard Practice
5) Graph the inequality below.
Bigger
Smaller a a ≥
– 3
– 3
Pacman eats the larger number.
Is the variable bigger or smaller?
Smaller
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

13. Pacman eats the larger number. Is the variable bigger or smaller?
Example
6) Graph the inequality below.
Bigger
Smaller a a ≥ 2 2
Pacman eats the larger number.
Is the variable bigger or smaller?
Smaller
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

14. Pacman eats the larger number. Is the variable bigger or smaller?
Whiteboard Practice
7) Graph the inequality below.
Bigger
Smaller
– 1
– 1
> y y
Pacman eats the larger number.
Is the variable bigger or smaller?
Smaller
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

15. Pacman eats the larger number. Is the variable bigger or smaller?
Example
8) Graph the inequality below.
Smaller
Bigger x x
<
Pacman eats the larger number.
Is the variable bigger or smaller?
Smaller
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

16. Pacman eats the larger number. Is the variable bigger or smaller?
Whiteboard Practice
9) Graph the inequality below.
Smaller
Bigger d d ≤
– 4
– 4
Pacman eats the larger number.
Is the variable bigger or smaller?
Smaller
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

17. Is the variable bigger or smaller? Pacman eats the larger number?
Example
10) Write the inequality for the graph below.
Smaller
Bigger
– 5 d -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10
Bigger
Smaller d ≤ ≥
– 5
Is the variable bigger or smaller?
Pacman eats the larger number?

18. Is the variable bigger or smaller? Pacman eats the larger number?
Whiteboard Practice
11) Write the inequality for the graph below.
Smaller
Bigger 8 y -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10
Smaller
Bigger y
<
> 8
Is the variable bigger or smaller?
Pacman eats the larger number?

19. Is the variable bigger or smaller? Pacman eats the larger number?
Example
12) Write the inequality for the graph below.
Smaller
Bigger
– 2 a -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10
Bigger
Smaller
– 2 ≤ ≥ a
Is the variable bigger or smaller?
Pacman eats the larger number?

20. Is the variable bigger or smaller? Pacman eats the larger number?
Whiteboard Practice
13) Write the inequality for the graph below.
Smaller
Bigger 7 x -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10
Smaller
Bigger 7
<
> x
Is the variable bigger or smaller?
Pacman eats the larger number?

21. Is the variable bigger or smaller? Pacman eats the larger number?
Example
14) Write the inequality for the graph below.
Smaller
Bigger
– 7 d -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10
Smaller
Bigger d
<
>
– 7
Is the variable bigger or smaller?
Pacman eats the larger number?

22. Is the variable bigger or smaller? Pacman eats the larger number?
Whiteboard Practice
15) Write the inequality for the graph below.
Smaller
Bigger a -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10
Smaller
Bigger ≤ ≥ a
Is the variable bigger or smaller?
Pacman eats the larger number?

23. Is the variable bigger or smaller? Pacman eats the larger number?
Example
16) Write the inequality for the graph below.
Smaller
Bigger 6 y -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10
Bigger
Smaller y
<
> 6
Is the variable bigger or smaller?
Pacman eats the larger number?

24. Is the variable bigger or smaller? Pacman eats the larger number?
Whiteboard Practice
17) Write the inequality for the graph below.
Smaller
Bigger 3 x -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10
Bigger
Smaller 3 ≤ ≥ x
Is the variable bigger or smaller?
Pacman eats the larger number?

25. Any number greater than or equal to 1.
Example
18) Write a solution to the inequality below.
Bigger x ≥ 1 x
is greater than or equal to 1. 1, 2, 3, …
Any number greater than or equal to 1.

26. Whiteboard Practice 19) Write a solution to the inequality below.
Smaller y
<
Bigger
– 4 y
is less than
– 4.
– 5,
– 6,
– 7, …
Any number less than – 4.

27. Any number greater than or equal to 7.
Example
20) Write a solution to the inequality below. 7 ≤
Bigger r r
is greater than or equal to 7. 7, 8, 9, …
Any number greater than or equal to 7.

28. Any number greater than – 2.
Whiteboard Practice
21) Write a solution to the inequality below.
– 2
<
Bigger k k
is greater than
– 2.
– 1, 0, 1, …
Any number greater than – 2.

29. Example 22) Does a solution of f = – 9 work for the inequality below.
Bigger
– 10
> f
– 10
>
– 9
Is – 10 greater than – 9? No -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

30. Is 4 less than or equal to – 1?
Whiteboard Practice
23) Does a solution of v = 4 work for the inequality below. 4 v ≤
Bigger
– 1 4 ≤
– 1
Is 4 less than or equal to – 1? No -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

31. Example 24) Does a solution of x = – 2 work for the inequality below.5
<
Bigger x 5
<
– 2
Is 5 less than – 2? No -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

32. Is 3 greater than or equal to 3?
Whiteboard Practice
25) Does a solution of b = 3 work for the inequality below. 3
Bigger b ≥ 3 3 ≥ 3
Is 3 greater than or equal to 3?
Yes -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

33. Is 7 greater than or equal to 8?
Whiteboard Practice
26) Does a solution of s = 7 work for the inequality below. 7
Bigger s ≥ 8 7 ≥ 8
Is 7 greater than or equal to 8? No -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

34. Example 27) Does a solution of p = – 6 work for the inequality below.
– 7
<
Bigger p
– 7
<
– 6
Is – 7 less than – 6?
Yes -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

35. Whiteboard Practice
28) Does a solution of e = – 3 work for the inequality below.
– 3
Bigger
– 4
> e
– 4
>
– 3
Is – 4 greater than – 3? No -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

36. Example 29) Does a solution of k = 2 work for the inequality below. 2≤
Bigger 3 2 ≤ 3
Is 2 less than or equal to 3?
Yes -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

37. Real World Application
30) For a regular driver’s license in Kansas a person has to be at least 17 years old. Write & graph an inequality for the driving age. 17 17
driving age
driving age
Bigger d ≤ ≥ 17 d d ≥ 17 17 9 7 5 3 1 11 13 15 17 19

38. Example 31) Solve the inequality. Check the solution. 3 + j ≤ 8
– 3
– 3
– 3 j ≤ 5

39. Checking the solution
31) Solve the inequality. Check the solution. 3 + j ≤ 8
3 + j ≤ 8
3 +
(5) j
≤ 8 8 ≤ 8 j ≤ 5 5

40. Whiteboard Practice
32) Solve the inequality. Check the solution. g – 4 > – 3
g – 4 > – 3
g – 4 > – 3 g
+ 4
+ 4
+ 4 g
> 1

41. Checking the solution
32) Solve the inequality. Check the solution. g – 4 > – 3
g – 4 > – 3
(2) g
– 4
> – 3
Bigger
– 2
>
– 3 g
> 1 1 2 2 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

42. Example 33) Solve the inequality. Check the solution. – 2 < h + 5
– 5
– 5
– 5
– 7
< h

43. Checking the solution
33) Solve the inequality. Check the solution. – 2 < h + 5
– 2 < h + 5
– 2
<
(– 6) h
+ 5
Bigger
– 2
<
– 1
– 7
– 7
< h
– 6
– 6 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

44. Whiteboard Practice
34) Solve the inequality. Check the solution. 1 ≥ r – 6
1 ≥ r – 6
1 ≥ r – 6 r
+ 6
+ 6
+ 6 7 ≥ r

45. Checking the solution
34) Solve the inequality. Check the solution. 1 ≥ r – 6
1 ≥ r – 6 1 ≥
(7) r
– 6 1 ≥ 1 7 7 ≥ r

46. Example 35) Solve the inequality. Check the solution. 5.8 < j + 3.5
– 3.5
– 3.5
– 3.5
2.3
< j

47. Checking the solution
35) Solve the inequality. Check the solution. 5.8 < j + 3.5
5.8 < j + 3.5
5.8
<
(2.4) j
+ 3.5
Bigger
5.8
<
5.9
2.3
2.3
< j
2.4
2.4 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

48. Whiteboard Practice
36) Solve the inequality. Check the solution. d – 2.7 > – 4.1
d – 2.7 > – 4.1 d
d – 2.7 > – 4.1
+ 2.7
+ 2.7
+ 2.7 d
>
– 1.4

49. Checking the solution
36) Solve the inequality. Check the solution. d – 2.7 > – 4.1
d – 2.7 > – 4.1
(– 1.3) d
– 2.7
> – 4.1
Bigger
– 4
>
– 4.1 d
>
– 1.4
– 1.4
– 1.3
– 1.3 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

50. Example
37) Solve the inequality. Check the solution. Graph the solution. – 9 ≤ x – 15
– 9 ≤ x – 15
– 9 ≤ x – 15 x
+ 15
+ 15
+ 15
Smaller 6 6 ≤ x x
Bigger -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

51. Checking the solution
37) Solve the inequality. Check the solution. Graph the solution. – 9 ≤ x – 15
– 9 ≤ x – 15
– 9 ≤
(6) x
– 15
– 9 ≤
– 9 6 6 ≤ x x

52. Whiteboard Practice
38) Solve the inequality. Check the solution. Graph the solution b > 7.2
11 + b > 7.2
11 + b > b
– 11
– 11
– 11
Bigger b b
>
– 3.8
– 3.8
Smaller -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

53. Checking the solution
38) Solve the inequality. Check the solution. Graph the solution b > 7.2
11 + b > 7.2
Bigger
11 +
(– 3.7) b
> 7.2
7.3
>
7.2 b
>
– 3.8
– 3.7
– 3.7 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10 1 2 3 4 5 6 7 8 9 10

54. Key Points & Don’t Forget
1) Make sure to use an inequality (<,>) & not an equal sign.
2) Check your solutions.
3) Make sure your graphs are pointing the right way.

55. The Assignment
pg #’s odd,
20-42 even, 45, 47

56. Bibliography
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