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Warmups
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Graph each solution set:
x  1andx  4
x  5orx  2
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A) define a variable b) write an inequality c) solve
Twice a number is greater than or equal to the number decreased by 5.
AND vs. OR Review
AND
OR
“and” or no word
Must say “or”
Both true
One or more true
Special case: No solution
Special case: All numbers
7-6 Absolute Value
“=“ & “<“
Objective: To solve open sentences involving
absolute value and graph their solutions.
Standards 3.0, 25.0
Absolute Value
|x| = 4
x = 4 or x = -4 |x| - 5 = 9
+5
+5
|x| = 14
x = 14 or x = -14
Set the inside of the absolute value equal to:
1. the number after the equal sign
2. negative the number after the equal sign
Example 1
|x - 3| = 4
x – 3 = 4 or x – 3 = -4
+3 +3
+ 3 +3
x=7
or x = -1
*When you graph with =, plot the points
Special Cases
1.
2.
|3 – 3x| = 0
3 – 3x = 0
-3
-3
-3x = -3
x=1
|10 – x| = -2
NO solution – cannot equal a negative!
“<” = AND less th”AN” is “AND”
|3 + 2x| < 11
Change:
• Inequality sign
• Make number after “<” negative
3 + 2x < 11 and 3 + 2x > -11
x < 4 and x > -7
Example 2 – Try with a partner
Change:
• Inequality sign
|n – 36| < 2
• Make number after “<” negative
n - 36 < 2 and n - 36 > -2
n < 38 and n > 34
Special Cases
1.
|4x - 12| < 0
2.
|2x + 8| < -2
No Solution
Let’s summarize…
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What do you do when you have an absolute
value set equal to an equal sign and a less
than inequality sign?
How many answers will you have when the
number after the inequality is positive, zero,
or negative?
Try with a partner…
1.
|11 – 3x| < 1
x > 10/3 and x < 4
2.
|3x + 9| < 0
No solution
3.
|2x + 5| < 5
x < 0 and x > -5
4.
|5 – 2x| < -5
No Solution
Homework
Pg. 424 # 17, 18, 19, 21, 23, 24, 25, 26,
29, 30, 31, 34
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