# Absolute Value Inequalities - PowerPoint by Udc4XK1S

VIEWS: 38 PAGES: 8

• pg 1
```									 Absolute
Value
Inequalities

Algebra
Solving an Absolute-Value Inequalities

x 6

8 7 6 5 4 3 2 1   0       1       2       3       4       5       6   7   8

x 6

8 7 6 5 4 3 2 1       0       1       2       3       4       5   6   7   8
Graphing Absolute Value
• When an absolute value is greater than
the variable you have a disjunction to
graph.      x 4
• When an absolute value is less than
the variable you have a conjunction to
graph.      x 4
Solving an Absolute-Value Inequality

Solve | x  4 | < 3

x  4 IS POSITIVE           x  4 IS NEGATIVE
|x4|3                     |x4|3
x  4  3                  x  4  3
x7                            x1
Reverse
inequality symbol.

The solution is all real numbers greater than 1 and less than 7.

This can be written as 1  x  7.
Solving an Absolute-Value Inequality

2x + 1  POSITIVE 2x the solution.
Solve | 2x IS1 | 3  6 and graph + 1 IS NEGATIVE
| 2x  1 |  3  6        | 2x  1 | 3  6
2x + 1 IS POSITIVE        2x + 1 IS NEGATIVE
| 2x|2x| 31 |6 9
1                | 2x|2x|  1 |6  9
1 3 
| 2x   |1  +9
2x 1  9                  2x |1  9
| 2x 1  9
2x  8
2x  1  +9
2x 10
2x  1 9
x4                         x  5
2x  8                      2x  10
The solution is all real numbers greater than or equal
x4                         x  5
to 4 or less than or equal Reverse can be written as
to  5. This
the compound inequality inequalityx  4.
x   5 or
symbol.

6 5 4 3 2 1         0   1   2   3   4   5   6
Strange Results

2(3x  8)  7  5          True for All Real Numbers,
since absolute value is
always positive, and
therefore greater than any
negative.

(2[3x  (8  4)]  12)3  2      No Solution Ø.
Positive numbers are
never less than
negative numbers.
Absolute
Value
Inequalities

Algebra

```
To top