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Section 1.7 – Solving Linear Inequalities
An inequality is similar to an equation except instead of an equal sign “=” you find one of
the following signs:
<,
≤
, >, or
≥
.
Now > and < are strict inequalities, and
≥
and
≤
are
inequalities that include equals (read these last two signs as ‘greater than or equal to’ and
‘less than or equal to,’ respectively).
The solutions will be different because a linear
equation has one, none, or many solutions.
A linear inequality has a solution that is over an
interval and the answers are in what is called
interval notation
.
This ensures that you have
the complete answer.
In this section, we will only be concerned with real number solutions.
Interval Notation:
Inequality
Interval Notation
A
x
<
( 29
A
,
∞

The rounded bracket means that A is not
included
A
x
≤
( ]
A
,
∞

The square bracket means that A is
included
B
x
( 29
∞
,
B
B
x
≥
[ 29
∞
,
B
B
x
A
<
<
( 29
B
A
,
B
x
A
≤
≤
[ ]
B
A
,
Intervals and the Number Line:
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 Spring '08
 Staff
 Inequalities

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