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Byju's Answer
Standard XII
Mathematics
Properties of Inequalities
The intervals...
Question
The interval(s) of
x
which satisfies the inequality
1
x
+
2
<
1
3
x
+
7
is/are
A
(
−
7
3
,
−
2
)
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B
(
−
2
,
∞
)
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C
(
−
5
2
,
−
7
3
)
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D
(
−
∞
,
−
5
2
)
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Solution
The correct options are
A
(
−
7
3
,
−
2
)
D
(
−
∞
,
−
5
2
)
1
x
+
2
<
1
3
x
+
7
⇒
1
x
+
2
−
1
3
x
+
7
<
0
⇒
3
x
+
7
−
x
−
2
(
x
+
2
)
(
3
x
+
7
)
<
0
⇒
2
x
+
5
(
x
+
2
)
(
3
x
+
7
)
<
0
Critical points are
−
5
2
,
−
7
3
,
−
2
Therefore,
x
∈
(
−
∞
,
−
5
2
)
∪
(
−
7
3
,
−
2
)
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0
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Standard XII Mathematics
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