The range of values for which x squared-7x+10<0
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Answer:
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Step-by-step explanation:
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Algebra Examples
Popular Problems Algebra Solve for x x^2-7x+10<0
x
2
−
7
x
+
10
<
0
Convert the inequality to an equation.
x
2
−
7
x
+
10
=
0
Factor
x
2
−
7
x
+
10
using the AC method.
(
x
−
5
)
(
x
−
2
)
=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
x
−
5
=
0
x
−
2
=
0
Set the first factor equal to
0
and solve.
x
=
5
Set the next factor equal to
0
and solve.
x
=
2
The final solution is all the values that make
(
x
−
5
)
(
x
−
2
)
=
0
true.
x
=
5
,
2
Use each root to create test intervals.
x
<
2
2
<
x
<
5
x
>
5
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
x
<
2
False
2
<
x
<
5
True
x
>
5
False
The solution consists of all of the true intervals.
2
<
x
<
5
The result can be shown in multiple forms.
Inequality Form:
2
<
x
<
5
Interval Notation:
(
2
,
5
)
image of graph