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Byju's Answer
Standard XII
Mathematics
Different Types of Intervals in Inequality
Find all valu...
Question
Find all values of
a
for which the inequality
x
−
2
a
−
3
x
−
a
+
2
<
0
is satisfied for all
x
belonging to the interval
1
⩽
x
⩽
2
.
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Solution
x
−
2
a
−
3
x
−
a
+
2
<
0
x
−
(
2
a
+
3
)
x
−
(
a
−
2
)
<
0
2
a
+
3
>
a
−
2
2
a
+
3
≥
2
2
a
≥
−
1
a
≥
−
1
2
a
−
2
≤
1
a
≤
−
3
a
ε
(
−
5
,
−
3
]
⋃
[
−
1
2
,
∞
)
when
2
a
+
3
<
a
−
2
a
<
−
5
a
−
2
≥
2
a
≥
4
(not possible)
2
a
+
3
≤
1
a
≤
−
1
a
ε
(
−
5
,
3
]
⋃
[
−
1
2
,
∞
)
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Different Types of Intervals in Inequality
Standard XII Mathematics
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