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Byju's Answer
Standard XI
Mathematics
Inequalities Involving Modulus Function
The number of...
Question
The number of integral solutions of the inequality
∣
∣
∣
1
−
|
x
|
1
+
|
x
|
∣
∣
∣
≥
1
2
,
is
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Solution
∣
∣
∣
1
−
|
x
|
1
+
|
x
|
∣
∣
∣
≥
1
2
⇒
∣
∣
∣
1
1
+
|
x
|
∣
∣
∣
≥
1
2
⇒
1
1
+
|
x
|
≥
1
2
(
∵
1
+
|
x
|
≥
1
)
⇒
1
+
|
x
|
≤
2
⇒
|
x
|
≤
1
∴
x
∈
[
−
1
,
1
]
Hence, number of integral solutions is
3.
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