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Byju's Answer
Standard XI
Mathematics
Properties of Inequalities
The number of...
Question
The number of integral values satisfying the inequality
(
x
+
2
)
(
x
−
7
)
(
x
+
3
)
4
<
0
is
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Solution
(
x
+
2
)
(
x
−
7
)
(
x
+
3
)
4
<
0
We know that
(
x
+
3
)
4
is always positive
So, the inequality becomes,
(
x
+
2
)
(
x
−
7
)
<
0
,
x
≠
−
3
⇒
x
∈
(
−
2
,
7
)
The required integral values are
{
−
1
,
0
,
1
,
2
,
3
,
4
,
5
,
6
}
Hence, number of integral values are
8
.
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