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Lessons 23
Sections 4.2 and
4.3
3part Inequality, Absolute Value Inequalities
3Part Inequality:
2
10
10
AND
2
x
x
x
< <
→
<
>
The number must meet both conditions, therefore the conjunction ‘and’.
Where are these numbers on the number line?
These numbers are
between
2 and 10.
This can be written as 2
10
x
< <
, a 3part
inequality.
Solve the following:
1)
12
4
3
12
≤
+
<

x
2)
10
3 2
0
x
> 
>
Examine this statement:
3
2
x
or x
< 
>
With an ‘or’ statement, only the first
condition or only the second condition must be true.
Where are these numbers on the
number line?
These are the numbers found in two ‘rays’ in opposite directions.
Many students try to
write this as a 3part inequality:
3
2
x
 > >
.
However, this implies
3
2
 >
, which is
false.
This type of situation is not a 3part inequality.
Examine:
2
<
x
Solutions include
87
.
1
,
999
.
1
,
8
7
1
,
2
3
,
1
,
0



These are the numbers that are less than 2
units from zero.
Examine where these are on a number line:
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 Spring '09
 Inequalities

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