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Byju's Answer
Standard XIII
Mathematics
Inequalities Involving Modulus Function
If |2x-5|>1, ...
Question
If
∣
∣
∣
2
x
−
5
∣
∣
∣
>
1
,
then
x
belongs to the interval
A
(
3
,
7
)
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B
(
3
,
5
)
∪
(
5
,
7
)
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C
[
3
,
7
]
−
{
5
}
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D
R
−
{
5
}
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Solution
The correct option is
B
(
3
,
5
)
∪
(
5
,
7
)
2
|
x
−
5
|
>
1
⇒
|
x
−
5
|
<
2
,
x
≠
5
⇒
−
2
<
x
−
5
<
2
,
x
≠
5
⇒
3
<
x
<
7
∴
x
∈
(
3
,
5
)
∪
(
5
,
7
)
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0
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