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Byju's Answer
Standard XII
Mathematics
Method of Intervals
The minimum v...
Question
The minimum value of x satisfying the inequality
4
−
x
+
0
.
5
−
7
⋅
2
−
x
≤
4
is
Open in App
Solution
Given
that
4
−
x
+
0
.
5
−
7
⋅
2
−
x
≤
4
.
.
.
.
[
1
]
Let
2
−
x
=
t
Now
[
1
]
can
be
written
as
2
t
2
−
7
t
≤
4
⇒
2
t
2
−
7
t
−
4
≤
0
⇒
2
t
2
−
8
t
+
t
−
4
≤
0
⇒
2
t
(
t
−
4
)
+
1
(
t
−
4
)
≤
0
⇒
(
t
−
4
)
(
2
t
+
1
)
≤
0
⇒
−
1
2
≤
t
≤
4
⇒
0
<
t
≤
4
(
A
s
t
=
2
−
x
a
n
d
2
−
x
>
0
)
⇒
0
<
2
−
x
≤
4
⇒
−
2
≤
x
<
∞
⇒
x
∈
[
−
2
,
∞
)
The minimum value of the given expression is -2.
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Q.
The minimum value of x satisfying the inequality
4
−
x
+
0
.
5
−
7
⋅
2
−
x
≤
4
is