Answer:

A.x < 2  or  x >  4

Step-by-step explanation:

x  2 − 6  x  +  8 > 0

Write the problem as a mathematical expression.

x 2 − 6 x + 8 > 0

Convert the inequality to an equation.

x 2 − 6 x + 8 = 0

Factor  

x 2 − 6 x + 8

using the AC method.

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( x − 4 ) ( 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 − 4 = 0 x − 2 = 0

Set  

x − 4

equal to  

0

and solve for  

x

.

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x

=

4

Set  

x

−

2

equal to  

0

and solve for  

x

.

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x

=

2

The final solution is all the values that make  

(

x

−

4

)

(

x

−

2

)

=

0

true.

x

=

4

,

2

Use each root to create test intervals.

x

<

2

2

<

x

<

4

x

>

4

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

<

2

True

2

<

x

<

4

False

x

>

4

True

The solution consists of all of the true intervals.

x

<

2

or  

x

>

4

The result can be shown in multiple forms.

Inequality Form:

x

<

2

or

x

>

4

Interval Notation:

(

−

∞

,

2

)

∪

(

4

,

∞

)

image of graph