Download Section 2-8 Absolute Value Inequalities

Absolute Value Inequalities
Section 2-8
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2-8: Absolute Value Inequalities
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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
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2-5: Graphing Linear Inequalities
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Steps for Solving and Graphing
Absolute Value Inequalities
1. Identify whether it is an AND/OR inequality
2. Write both equations with one with the
regular sign and other equation with the sign
SWITCHED with OPPOSITE number
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2-8: Absolute Value Inequalities
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Solving for Absolute Value
Inequalities
When Solving for Inequalities, remember:
Less ThAND
Less Than, “AND”
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GreatOR Than
Greater Than, “OR”
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Example 5
Solve | x  3 | 5 and graph the solution
AND
5  x  3  5
8  x  2
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–8
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2-8: Absolute Value Inequalities
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Example 6
Solve | 4 x  5 | 13 and graph the solution
4x  5  13
4x  8
x2
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|
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-5 –9/2 -4
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OR
4x  5  13
4x  18
9
x
2
9
x  2 or x  
2
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0
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Example 7
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x 2 5  3
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Solve
and graph the solution
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x 2  8
7
1
8  x  2  8
7
1
10  x  6
7
70  x  42
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Example 8
Solve 3 12  4 x  4  28
3 12  4 x  4  28
4 4
3 12  4 x  24
3 12  4 x 24

3
3
12  4 x  8
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Example 8
12  4 x  8
8  12  4 x  8
12 12
12
20  4 x  4
20 4 x 4


4
4
4
5  x 1
1 x  5
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Example 10
Solve 8 x  4  48
8 x  4 48

8
8
x 4 6
x 4 6
x 2
OR
x  4  6
x  10
x  2 OR x  10
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Example 11
Solve | 2 x  1| 25 and graph the solution
| 2 x  1 |  25
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0
No Solution
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Example 12
Solve | x  1 | 16 and graph the solution
| x  1 |  16
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0
All Real Numbers
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Your Turn
Solve | 2 x  5 | x  1 and graph the solution on
a number line
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x  or x  6
3
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Your Turn
Solve 2 x  4  22 and graph the solution
All Real Numbers
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Example 10
Solve
4x  8
8
3
8  x  4
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Assignment
Pg 154
14, 15, 17-47 odd, 22, 26, omit 43
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