Answer:
|
3
x
+
5
|
=
5
x
+
2
Remove the absolute value term. This creates a
±
on the right side of the equation because
|
x
|
=
±
x
.
3
x
+
5
=
±
(
5
x
+
2
)
Set up the positive portion of the
±
solution.
3
x
+
5
=
5
x
+
2
Solve the first equation for
x
.
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x
=
3
2
Set up the negative portion of the
±
solution.
3
x
+
5
=
−
(
5
x
+
2
)
Solve the second equation for
x
.
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x
=
−
7
8
The solution to the equation includes both the positive and negative portions of the solution.
x
=
3
2
,
−
7
8
Exclude the solutions that do not make
|
3
x
+
5
|
=
5
x
+
2
true.
x
=
3
2
The result can be shown in multiple forms.
Exact Form:
x
=
3
2
Decimal Form:
x
=
1.5
Mixed Number Form:
x
=
1
1
2
