Solve the inequality.
1. 3x+2>5x-8
Answers
Answer:
Explanation:
3
x
2
−
5
x
>
8
Subtract
8
from both sides:
3
x
2
−
5
x
−
8
>
0
We now solve the equation:
3
x
2
−
5
x
−
8
=
0
This will give us the boundary values of
x
.
Factoring:
(
3
x
−
8
)
(
x
+
1
)
=
0
⇒
x
=
−
1
and
x
=
8
3
METHOD 1
From:
3
x
2
−
5
x
−
8
>
0
Notice that the coefficient of
x
2
>
0
, this means the parabola is in this form:
⋃
For values greater than
0
we will be above the
x
axis.
Since the roots to the equation are on the
x
axis we can see that for positive
y
values we will be to the left of
x
=
−
1
and to the right of
x
=
8
3
.
Since this is a
>
and not a
≥
inequality
x
=
−
1
and
x
=
8
3
are not included points. So the solution in interval notation we be a union of intervals:
(
−
∞
,
−
1
)
∪
(
8
3
,
∞
)
METHOD 2
Using the factors of
3
x
2
−
5
x
−
8
>
0
we found earlier, we can see that:
(
3
x
−
8
)
(
x
+
1
)
Will be positive i.e.
>
0
if both brackets are positive or both brackets are negative. We can use a table to check this using the following inequalities:
x
<
−
1
,
88
−
1
<
x
<
8
3
,
88
8
3
<
x
enter image source here
You can see from the table that if we assign
x
a value satisfying the inequality in each column. it is only for the inequalities
x
>
−
1
and
8
3
<
x
that the product of the brackets is positive.
So our solution in interval notation is:
(
−
∞
,
−
1
)
∪
(
8
3
,
∞
)
as before.
Graph
graph{y<3x^2-5x-8 [-32.48, 32.46, -16.24, 16.25]}
Step-by-step explanation:
I hope it will help you if it is right then follow me
Answer:
3x+2>5x-8
3x - 3x +2>5x - 3x -8
2 > 2x - 8
2 + 8 > 2x
10 > 2x
x < 5