find inequality x(x-3) (x-5)<0
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1
Answer:
In order for this inequality to be true, you need
(
x
−
3
)
and
(
x
−
5
)
to either both be positive or both be negative.
For any value of
x
>
5
you will get
{
x
−
3
>
0
x
−
5
>
0
⇒
(
x
−
3
)
(
x
−
5
)
>
0
For any value of
x
<
3
you will get
{
x
−
3
<
0
x
−
5
<
0
⇒
(
x
−
3
)
(
x
−
5
)
>
0
This inequality will thus be satisfied for any value of
x
∈
(
−
∞
,
3
)
∪
(
5
,
+
∞
)
.
On the other hand, any value of
x
∈
[
3
,
5
]
will not be a valid solution.
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