2x + 3/
(x-1) (x - 2)
Answers
Answered by
0
Answer:
hjpjbrfjtgjhhhgggbudgiiy
Answered by
0
Answer:
The solutions are
S
=
{
1
,
3
2
}
Explanation:
The equation is
|
2
x
−
3
|
+
|
x
−
1
|
=
|
x
−
2
|
There are
3
points to consider
⎧
⎪
⎨
⎪
⎩
2
x
−
3
=
0
x
−
1
=
0
x
−
2
=
0
⇒
,
⎧
⎪
⎪
⎨
⎪
⎪
⎩
x
=
3
2
x
=
1
x
=
2
There are
4
intervals to consider
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
−
∞
1
1
3
2
3
2
2
2
+
∞
On the first interval
(
−
∞
,
1
)
−
2
x
+
3
−
x
+
1
=
−
x
+
2
⇒
,
2
x
=
2
⇒
,
x
=
1
x
fits in this interval and the solution is valid
On the second interval
(
1
,
3
2
)
−
2
x
+
3
+
x
−
1
=
−
x
+
2
⇒
,
0
=
0
There is no solution in this interval
On the third interval
(
3
2
,
2
)
2
x
−
3
+
x
−
1
=
−
x
+
2
⇒
,
4
x
=
6
⇒
,
x
=
6
4
=
3
2
x
fits in this interval and the solution is valid
On the fourth interval
(
2
,
+
∞
)
2
x
−
3
+
x
−
1
=
x
−
2
⇒
,
2
x
=
2
⇒
,
x
=
1
x
does not fit in this interval.
The solutions are
S
=
{
1
,
3
2
}
Similar questions