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4 votes
Solve |5 - 8x| - 7 < 8



2 Answers

3 votes
Solve for
x
x
by simplifying both sides of the inequality, then isolating the variable.
Inequality Form:

5
4
<
x
<
5
2
-
5
4
<
x
<
5
2
Interval Notation:
(

5
4
,
5
2
)
User Nicocesar
by
7.6k points
2 votes
Move all terms not containing
|
5

8
x
|
|
5
-
8
x
|
to the right side of the inequality.
Tap for fewer steps...
Add
7
7
to both sides of the inequality.
|
5

8
x
|
<
8
+
7
|
5
-
8
x
|
<
8
+
7
Add
8
8
and
7
7
.
|
5

8
x
|
<
15
|
5
-
8
x
|
<
15
Remove the absolute value term. This creates a
±
±
on the right side of the inequality because
|
x
|
=
±
x
|
x
|
=
±
x
.
5

8
x
<
±
15
5
-
8
x
<
±
15
Set up the positive portion of the
±
±
solution.
5

8
x
<
15
5
-
8
x
<
15
Solve the first inequality for
x
x
.
Tap for more steps...
x
>

5
4
x
>
-
5
4
Set up the negative portion of the
±
±
solution. When solving the negative portion of an inequality, flip the direction of the inequality sign.
5

8
x
>

15
5
-
8
x
>
-
15
Solve the second inequality for
x
x
.
Tap for more steps...
x
<
5
2
x
<
5
2
Set up the intersection.
x
>

5
4
x
>
-
5
4
and
x
<
5
2
x
<
5
2
Find the intersection between the sets.

5
4
<
x
<
5
2
-
5
4
<
x
<
5
2
The result can be shown in multiple forms.
Inequality Form:

5
4
<
x
<
5
2
-
5
4
<
x
<
5
2
Interval Notation:
(

5
4
,
5
2
)
(
-
5
4
,
5
2
)

User TofferJ
by
8.2k points

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