(x-3)(x-5)<_0
If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.
x−3=0x-3=0
x+5=0x+5=0
Set the first factor equal to 00 and solve.
x=3x=3
Set the next factor equal to 00 and solve.
x=−5x=-5
Consolidate the solutions.
x=3,−5x=3,-5
Use each root to create test intervals.
x<−5x<-5
−5<x<3-5<x<3
x>3x>3
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
x<−5x<-5 False
−5<x<3-5<x<3 True
x>3x>3 False
The solution consists of all of the true intervals.
−5<x<3-5<x<3
The result can be shown in multiple forms.
Inequality Form:
−5<x<3-5<x<3
Interval Notation:
(−5,3)
