81
L9 Solving Inequalities
Inequalities Involving Absolute Value
1. Open Intervals
Graphs
Interval Notation
x
a
>
a
x
b
<
<
x
b
<
2. Half-open Intervals
x
a
≥
x
b
≤
a
x
b
≤
<
3. Closed Intervals
a
x
b
≤
≤
4. All real numbers
(
)
\
x
−∞ <
< +∞
82
Properties of Inequalities
:
1.
Transitive Property
If
a
b
<
and
b
c
<
, then
2.
Addition of Inequalities
If
a
b
<
and
c
d
<
, then
3.
Addition of a Constant
c
If
a
b
<
, then
4.
Multiplying by a Constant
c
If
a
b
<
and
0
c
>
, then
If
a
b
<
and
0
c
<
, then
Note
:
When multiplying or dividing both sides by a
negative
number, reverse
the direction of the
inequality.

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