1. 1.6: Solve Linear Inequalities
Page 30 3) 5) 7)
y = –3x + 26; y = 5 9)
y = –6/5x + 31/5; y = 11
11)
y = 3/2x – 21/2; y = –3
13)
y = 7/4x – 11/4; y = 6
15) C
17)
There are two y’s on both sides
19)
21)
23)
25)
29)
Omit
31)
omit
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1.6: Solve Linear Inequalities

2. 1.6: Solve Linear Inequalities
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1.6: Solve Linear Inequalities

3. 1.6: Solve Linear Inequalities
Page 37 3)
t = 0.5h 5)
d = 90 miles 7)
P = 54 feet 9)
w = 20 meters
11)
y = 4x + 11
13)
y = –10x + 46
15) D
21) B
24)
mi/hr
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1.6: Solve Linear Inequalities

4. SOLVE LINEAR INEQUALITIES Section 1.6 4 11/20/2018 8:04 AM

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

6. 1.6: 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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1.6: Solve Linear Inequalities

7. 1.6: 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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1.6: Solve Linear Inequalities

8. 1.6: 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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1.6: Solve Linear Inequalities

9. 1.6: Solve Linear Inequalities
Set-Builder Notation
A representative set is a collection of items
{ x | x > 0 } reads “the set of all x such that x is greater than zero”
Applies to inequalities
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1.6: Solve Linear Inequalities

10. 1.6: 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
Less thAND: Shade towards or INSIDE
GreatOR: Shade away or OUTSIDE
REMEMBER: When we NEGATIVE DIVIDE, we FLIP THE SIGN
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1.6: Solve Linear Inequalities

11. 1.6: Solve Linear Inequalities
Example 1
Solve 2x < 12, graph and label as an inequality, set-builder notation, and internal notation.
Make sure to shade the triangle for infinity | | 6
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1.6: Solve Linear Inequalities

12. 1.6: Solve Linear Inequalities
Example 2
Solve x + 8 > 4x + 17, graph and label as an inequality, set-builder notation, and internal notation. | –3 |
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1.6: Solve Linear Inequalities

13. 1.6: Solve Linear Inequalities
Your Turn
Solve –2 > –12x + 8, graph and label as an inequality, set-builder notation, and internal notation. |
5/6
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1.6: Solve Linear Inequalities

14. 1.6: Solve Linear Inequalities
Example 3
Solve –4 < 6x – 10 < 14, graph and label as an inequality, set-builder notation, and internal notation. | | 1 | 4
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1.6: Solve Linear Inequalities

15. 1.6: Solve Linear Inequalities
Your Turn
Solve 0 < 3/4x + 3 < 4, graph and label as an inequality, set-builder notation, and internal notation. | –4 | |
4/3
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1.6: Solve Linear Inequalities

16. 1.6: Solve Linear Inequalities
Example 4
Solve 2x – 1 < –7 or 4x + 3 > 7, graph and label as an inequality, set-builder notation, and internal notation. | –3 | | 1
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1.6: Solve Linear Inequalities

17. 1.6: Solve Linear Inequalities
Example 5
Solve x + 5 < 10 OR x – 2 > 1, graph and label as an inequality, set-builder notation, and internal notation. | | 3 | 5
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1.6: Solve Linear Inequalities

18. 1.6: Solve Linear Inequalities
Example 6
Solve 5x – 10 < 5(x + 2)
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1.6: Solve Linear Inequalities

19. 1.6: Solve Linear Inequalities
Your Turn
Solve 6(x – 2) > 3(2x – 1)
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1.6: Solve Linear Inequalities

20. 1.6: Solve Linear Inequalities
Example 7
A lizard has a temperature that ranges from 18°C to 34°C. Write the range of temperatures as a compound inequality. Then write an inequality giving the temperature range in degrees in Fahrenheit. The conversion of Celsius to Fahrenheit is 5/9(F – 32).
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1.6: Solve Linear Inequalities

21. 1.6: Solve Linear Inequalities
Your Turn
In Illinois, the lowest temperature on record is –36°F in January The highest temperature was recorded in East St. Louis at 117°F. Determine the range of temperatures in Celsius. The conversion of Celsius is 9/5C + 32.
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1.6: Solve Linear Inequalities

22. 1.6: Solve Linear Inequalities
Assignment
Pg 44: 3-15 odd, odd, all, 53, 56
29-45: With the inequality, write out in set-builder notation and interval notation
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1.6: Solve Linear Inequalities