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Standard VIII
Mathematics
Question
Solve:
1
|
x
|
−
5
≤
1
3
Open in App
Solution
Verified by Toppr
Given,
1
|
|
x
|
−
5
≤
1
3
Case I:
x
≥
0
⇒
|
x
|
=
x
1
x
−
5
−
1
3
≤
0
⇒
3
−
x
+
5
3
(
x
−
5
)
≤
0
⇒
x
−
8
x
−
5
≥
0
x
∈
(
−
∞
,
5
)
∪
(
8
,
∞
)
As
x
≥
0
⇒
x
∈
[
0
,
5
]
∪
[
8
,
∞
]
−
−
−
(
1
)
Case II:
x
<
0
⇒
|
x
|
=
−
x
1
−
x
−
5
≤
1
3
⇒
1
3
+
1
x
+
5
≥
0
⇒
x
+
8
x
+
5
≥
0
x
∈
(
−
∞
,
−
8
)
∪
(
−
5
,
∞
)
As
x
<
0
,
⇒
x
∈
(
−
∞
,
8
)
∪
(
−
5
,
0
)
−
−
−
(
2
)
x
∈
(
−
∞
,
−
8
)
∩
(
−
5
,
5
)
∪
(
8
,
∞
)
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