Answer:
2
3
x
+
14
−
3
x
>
4
−
3
x
7
Write the problem as a mathematical expression.
2
3
x
+
14
−
3
x
>
4
−
3
x
7
Graph each side of the equation. The solution is the x-value of the point of intersection.
x
≈
−
1.23527136
Find the domain of
2
3
x
−
3
x
+
10
+
3
x
7
.
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(
−
∞
,
0
)
∪
(
0
,
∞
)
Use each root to create test intervals.
x
<
−
1.23527136
−
1.23527136
<
x
<
0
x
>
0
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
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x
<
−
1.23527136
False
−
1.23527136
<
x
<
0
True
x
>
0
True
The solution consists of all of the true intervals.
−
1.23527136
<
x
<
0
or
x
>
0
The result can be shown in multiple forms.
Inequality Form:
−
1.23527136
<
x
<
0
or
x
>
0
Interval Notation:
(
−
1.23527136
,
0
)
∪
(
0
,
∞
)
image of graph
