2. Find the value of x
3x +7

(x-3)/(x-7)>0

Step-by-step explanation: Find all the values where the expression switches from negative to positive by setting each factor equal to

0

and solving.

x−3=0

x−7=0

Add 3 to both sides of the equation.

x = 3

Add 7 to both sides of the equation.

x =7

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

x = 3

x = 7

Consolidate the solutions.

x = 3, 7

Find the domain of x−3x−7.

Find the domain of  x −3x−7.

Set the denominator in

x−3x−7

equal to 0

to find where the expression is undefined.

x−7=0

Add 7 to both sides of the equation.

x=7

The domain is all values of x

that make the expression defined.

Interval Notation:

(−∞,7)∪(7,∞)

Use each root to create test intervals.

x< 3

3<x<7x

>7

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

x< 3 True

3<x<7 False

x>7 True

The solution consists of all of the true intervals.

x<3 or x>7

The result can be shown in multiple forms.

Inequality Form:

x< 3 or x>7

Interval Notation:

(−∞,3)∪(7,∞)