Answer: (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,∞)
