What is the solution to the equation = ? x = 1 x = 2 x = 4 x = 6

4

<

x

<

6

Step-by-step explanation:

Move  

1

x

−

6

to the left side of the equation by subtracting it from both sides.

1

x

−

4

−

1

x

−

6

>

0

To write  

1

x

−

4

as a fraction with a common denominator, multiply by  

x

−

6

x

−

6

.

1

x

−

4

⋅

x

−

6

x

−

6

−

1

x

−

6

>

0

To write  

−

1

x

−

6

as a fraction with a common denominator, multiply by  

x

−

4

x

−

4

.

1

x

−

4

⋅

x

−

6

x

−

6

−

1

x

−

6

⋅

x

−

4

x

−

4

>

0

Write each expression with a common denominator of  

(

x

−

4

)

(

x

−

6

)

, by multiplying each by an appropriate factor of  

1

.

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1

(

x

−

6

)

(

x

−

4

)

(

x

−

6

)

−

1

(

x

−

4

)

(

x

−

4

)

(

x

−

6

)

>

0

Combine the numerators over the common denominator.

1

(

x

−

6

)

−

(

x

−

4

)

(

x

−

4

)

(

x

−

6

)

>

0

Simplify the numerator.

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−

2

(

x

−

4

)

(

x

−

6

)

>

0

Move the negative in front of the fraction.

−

2

(

x

−

4

)

(

x

−

6

)

>

0

Find all the values where the expression switches from negative to positive by setting each factor equal to  

0

and solving.

x

−

4

=

0

x

−

6

=

0

Add  

4

to both sides of the equation.

x

=

4

Add  

6

to both sides of the equation.

x

=

6

Solve for each factor to find the values where the absolute value expression goes from negative to positive.

x

=

4

x

=

6

Consolidate the solutions.

x

=

4

,

6

Find the domain of  

−

2

(

x

−

4

)

(

x

−

6

)

.

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Interval Notation:

(

−

∞

,

4

)

∪

(

4

,

6

)

∪

(

6

,

∞

)

Use each root to create test intervals.

x

<

4

4

<

x

<

6

x

>

6

The answer is 4 I hope this helps

answer: what equations are there

step-by-step explanation: