1. 6.1: Solve Linear Inequalities
Do NOW
Plug this into your graphing calculator and determine the equation. Then, identify whether type correlation it is.
Years of Education
Income 19
125,000 20
100,000 16
40,000
35,000 18
41,000 12
29,000 14
24,000
50,000 17
60,000
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6.1: Solve Linear Inequalities

2. 6.1: Solve Linear Inequalities
Worksheet Key
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6.1: Solve Linear Inequalities

3. 6.1: Solve Linear Inequalities
Worksheet Key
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6.1: Solve Linear Inequalities

4. 6.1: Solve Linear Inequalities
Worksheet Key
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6.1: Solve Linear Inequalities

5. 6.1: Solve Linear Inequalities
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6.1: Solve Linear Inequalities

6. SOLVE LINEAR INEQUALITIES Section 6.1 6 11/20/2018 8:03 AM

7. What do these signs mean?
>
Greater than ≥
Greater than OR equal to
<
Less than
Less than OR equal to ≤
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6.1: Solve Linear Inequalities

8. 6.1: Solve Linear Inequalities
Key Words
Greater Than, ‘ > ’ sign
Greater Than
Bigger Than
Less Than, ‘ < ’ sign
Less Than
Smaller Than
Greater Than or Equal to, ‘ > ’ sign
Greater Than or Equal to
Minimum of
At least
No less than
Less Than or Equal to, ‘ < ’ sign
Less Than or Equal to
Maximum of
Up to
No More Than
At Most
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6.1: Solve Linear Inequalities

9. 6.1: Solve Linear Inequalities
Example 1
Your sister gave you her credit card and said that you could go shopping for a birthday present for your significant other. She said that you could spend no more than $125. Write the expression.
What are some amounts that you could spend?
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6.1: Solve Linear Inequalities

10. 6.1: Solve Linear Inequalities
Your Turn
Your sister gave you her credit card and said that you could go shopping for a birthday present for your significant other. She said that you could spend at least $125. Write the expression.
What are some amounts that you could spend?
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6.1: Solve Linear Inequalities

11. 6.1: Solve Linear Inequalities
Example 2
Is (2, 4) a solution to the inequality y < 2x + 1?
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6.1: Solve Linear Inequalities

12. 6.1: Solve Linear Inequalities
Example 3
Is (2, –4) a solution to the inequality y > 2x + 1?
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6.1: Solve Linear Inequalities

13. 6.1: Solve Linear Inequalities
Example 4
Is (2, 5) a solution to the inequality y < 2x + 1?
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6.1: Solve Linear Inequalities

14. 6.1: Solve Linear Inequalities
Your Turn
Is (–3, –4) a solution to the inequality 2y > 3x + 1?
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6.1: Solve Linear Inequalities

15. 6.1: Solve Linear Inequalities
Definitions
Inequality is an equation where the variable does not equal to each other
>, <, or ≠ requires the dot being OPEN
>, <, or = required the dot being CLOSED hole
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6.1: Solve Linear Inequalities

16. 6.1: Solve Linear Inequalities
X typically comes first or is in the middle of the compound
> represents greater than
< represents less than
<, > represents greater than or equal to, less than or equal to
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6.1: Solve Linear Inequalities

17. 6.1: Solve Linear Inequalities
Interval Notation
Smallest number, bigger number
Brackets [ , ] represents greater than or equal to, less than or equal to
Parenthesis ( , ) represents greater than or less than
On the ends, extremes use infinity: ∞; always deals with parenthesis
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6.1: Solve Linear Inequalities

18. 6.1: Solve Linear Inequalities
Steps
Put the variables onto one side
Divide the number(s) in front of the variable
Graph on a number line based on the inequality given
Follow the arrow of the expression IF the variable comes first
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6.1: Solve Linear Inequalities

19. 6.1: Solve Linear Inequalities
Example 5
Solve x < 6, graph and label as an inequality and internal notation.
Make sure to shade the triangle for infinity | | 6
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6.1: Solve Linear Inequalities

20. 6.1: Solve Linear Inequalities
Example 6
Solve 2x – 8 > 6, graph and label as an inequality and internal notation. | | 7
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6.1: Solve Linear Inequalities

21. 6.1: Solve Linear Inequalities
Example 7
Solve , graph and label as an inequality and internal notation. |
–4 1/4 |
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6.1: Solve Linear Inequalities

22. 6.1: Solve Linear Inequalities
Your Turn
Solve x + 4 > –5, graph and label as an inequality and internal notation. | –9 |
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6.1: Solve Linear Inequalities

23. 6.1: Solve Linear Inequalities
Example 8
Solve –1 > x – 1/2, graph and label as an inequality and internal notation. |
–1/2 |
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6.1: Solve Linear Inequalities

24. 6.1: Solve Linear Inequalities
Example 9
Solve 5x + 3 > 4x + 5 , graph and label as an inequality. | | 2
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6.1: Solve Linear Inequalities

25. 6.1: Solve Linear Inequalities
Your Turn
Solve 5x – 6 < 4x – 4 , graph and label as an inequality. | | 2
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6.1: Solve Linear Inequalities

26. 6.1: Solve Linear Inequalities
Rule
REMEMBER: When we NEGATIVE DIVIDE, we FLIP THE SIGN
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6.1: Solve Linear Inequalities

27. Example 10
Solve –3x > 24, graph and label as an inequality and internal notation.
When we negative divide, we flip the sign | –8 |
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6.1: Solve Linear Inequalities

28. Example 11
Solve –3/4x > 18, graph and label as an inequality and internal notation.
When we negative divide, we flip the sign |
–24 |
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6.1: Solve Linear Inequalities

29. 6.1: Solve Linear Inequalities
Example 12
Solve x + 8 > 4x + 17, graph and label as an inequality | –3 |
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6.1: Solve Linear Inequalities

30. 6.1: Solve Linear Inequalities
Your Turn
Solve , write the answer as an inequality, and graph on a number line |
–36 |
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6.1: Solve Linear Inequalities

31. 6.1: Solve Linear Inequalities
Do NOW
Tell whether the order pair is a solution to the inequality. Show all work:
Solve the inequalities, graph, and write the answer in Inequality and Interval Notation form
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6.1: Solve Linear Inequalities

32. 6.1: Solve Linear Inequalities
Worksheet Key
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6.1: Solve Linear Inequalities

33. 6.1: Solve Linear Inequalities
Worksheet Key
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6.1: Solve Linear Inequalities

34. 6.1: Solve Linear Inequalities
Quiz
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6.1: Solve Linear Inequalities

35. Graphing Inequalities
Draw the graph either applying slope–intercept or quick graph form
When using “cover–up,” if there is a negative coefficient in the y, flip the direction of the graph
Determine what the sign is and graph the line
Dotted Line: Greater, Less, or not–equal to
Solid Line: Greater then OR equal to, Less than OR equal to, Equal to
Shade above or below the line by looking at inequality
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6.1: Solve Linear Inequalities

36. Graphing Inequalities
>
>
Greater than
Greater than OR equal to
<
<
Less than
Less than OR equal to
Dotted Line
Solid Line

37. 6.1: Solve Linear Inequalities
Example 13
Graph x < 4
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6.1: Solve Linear Inequalities

38. 6.1: Solve Linear Inequalities
Example 14
Graph x > 1
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6.1: Solve Linear Inequalities

39. 6.1: Solve Linear Inequalities
Your Turn
Graph x < 0
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6.1: Solve Linear Inequalities

40. Steps in Graphing
shade
Greater Than u
>
>

41. Steps in Graphing
shade
own
<
<
Less Than

42. 6.1: Solve Linear Inequalities
Example 15
Graph y < –2
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6.1: Solve Linear Inequalities

43. 6.1: Solve Linear Inequalities
Example 16
Graph y < x + 1
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6.1: Solve Linear Inequalities

44. Example 16 Calculator Check
Graph y < x + 1
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6.1: Solve Linear Inequalities

45. 6.1: Solve Linear Inequalities
Example 17
Graph 2x + 2y < –2
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6.1: Solve Linear Inequalities

46. 6.1: Solve Linear Inequalities
Your Turn
Graph 3x + y > –2
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6.1: Solve Linear Inequalities

47. 6.1: Solve Linear Inequalities
Example 18
Graph 2x – y < 2
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6.1: Solve Linear Inequalities

48. 6.1: Solve Linear Inequalities
Example 19
Graph 2x – 4y < 8
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6.1: Solve Linear Inequalities

49. 6.1: Solve Linear Inequalities
Your Turn
Graph 3x – 2y < 8
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6.1: Solve Linear Inequalities

50. 6.1: Solve Linear Inequalities
Assignment
Worksheet
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6.1: Solve Linear Inequalities