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Manipal Entrance Test 2019 Math Paper
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© examsnet.com
Question : 39
Total: 70
If
3
x
+
2
2
x
≥
5
x
,
then the solution set for
x
is
(
−
∞
,
2
]
[
2
,
∞
)
[
0
,
2
]
{
2
}
Validate
Solution:
We have,
3
x
+
2
2
x
≥
5
x
3
x
+
(
2
2
)
x
≥
5
x
;
3
x
+
4
x
≥
5
x
⇒
(
3
5
)
x
+
(
4
5
)
x
≥
1
⇒
(
sin
θ
)
x
+
(
cos
θ
)
x
≥
1
[by triangle inequality]
⇒
x
≤
2
∴ Solution set is
(
−
∞
,
2
]
© examsnet.com
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